Small separations in pinch-graphic matroids

Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial...
Ausführliche Beschreibung

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Autor*in:	Guenin, Bertrand [verfasserIn] Heo, Cheolwon

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Binary matroids Signed-graphs Grafts Algorithms Complexity

Anmerkung:	© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Mathematical programming - Berlin : Springer, 1971, 204(2023), 1-2 vom: 19. Apr., Seite 81-111
Übergeordnetes Werk:	volume:204 ; year:2023 ; number:1-2 ; day:19 ; month:04 ; pages:81-111

Links:	Volltext

DOI / URN:	10.1007/s10107-023-01950-8

Katalog-ID:	SPR054780144

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520			\|a Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids.
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allfields	10.1007/s10107-023-01950-8 doi (DE-627)SPR054780144 (SPR)s10107-023-01950-8-e DE-627 ger DE-627 rakwb eng Guenin, Bertrand verfasserin (orcid)0000-0001-8661-6196 aut Small separations in pinch-graphic matroids 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids. Binary matroids (dpeaa)DE-He213 Signed-graphs (dpeaa)DE-He213 Grafts (dpeaa)DE-He213 Algorithms (dpeaa)DE-He213 Complexity (dpeaa)DE-He213 Heo, Cheolwon aut Enthalten in Mathematical programming Berlin : Springer, 1971 204(2023), 1-2 vom: 19. Apr., Seite 81-111 (DE-627)25491179X (DE-600)1463397-8 1436-4646 nnns volume:204 year:2023 number:1-2 day:19 month:04 pages:81-111 https://dx.doi.org/10.1007/s10107-023-01950-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 204 2023 1-2 19 04 81-111
spelling	10.1007/s10107-023-01950-8 doi (DE-627)SPR054780144 (SPR)s10107-023-01950-8-e DE-627 ger DE-627 rakwb eng Guenin, Bertrand verfasserin (orcid)0000-0001-8661-6196 aut Small separations in pinch-graphic matroids 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids. Binary matroids (dpeaa)DE-He213 Signed-graphs (dpeaa)DE-He213 Grafts (dpeaa)DE-He213 Algorithms (dpeaa)DE-He213 Complexity (dpeaa)DE-He213 Heo, Cheolwon aut Enthalten in Mathematical programming Berlin : Springer, 1971 204(2023), 1-2 vom: 19. Apr., Seite 81-111 (DE-627)25491179X (DE-600)1463397-8 1436-4646 nnns volume:204 year:2023 number:1-2 day:19 month:04 pages:81-111 https://dx.doi.org/10.1007/s10107-023-01950-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 204 2023 1-2 19 04 81-111
allfields_unstemmed	10.1007/s10107-023-01950-8 doi (DE-627)SPR054780144 (SPR)s10107-023-01950-8-e DE-627 ger DE-627 rakwb eng Guenin, Bertrand verfasserin (orcid)0000-0001-8661-6196 aut Small separations in pinch-graphic matroids 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids. Binary matroids (dpeaa)DE-He213 Signed-graphs (dpeaa)DE-He213 Grafts (dpeaa)DE-He213 Algorithms (dpeaa)DE-He213 Complexity (dpeaa)DE-He213 Heo, Cheolwon aut Enthalten in Mathematical programming Berlin : Springer, 1971 204(2023), 1-2 vom: 19. Apr., Seite 81-111 (DE-627)25491179X (DE-600)1463397-8 1436-4646 nnns volume:204 year:2023 number:1-2 day:19 month:04 pages:81-111 https://dx.doi.org/10.1007/s10107-023-01950-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 204 2023 1-2 19 04 81-111
allfieldsGer	10.1007/s10107-023-01950-8 doi (DE-627)SPR054780144 (SPR)s10107-023-01950-8-e DE-627 ger DE-627 rakwb eng Guenin, Bertrand verfasserin (orcid)0000-0001-8661-6196 aut Small separations in pinch-graphic matroids 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids. Binary matroids (dpeaa)DE-He213 Signed-graphs (dpeaa)DE-He213 Grafts (dpeaa)DE-He213 Algorithms (dpeaa)DE-He213 Complexity (dpeaa)DE-He213 Heo, Cheolwon aut Enthalten in Mathematical programming Berlin : Springer, 1971 204(2023), 1-2 vom: 19. Apr., Seite 81-111 (DE-627)25491179X (DE-600)1463397-8 1436-4646 nnns volume:204 year:2023 number:1-2 day:19 month:04 pages:81-111 https://dx.doi.org/10.1007/s10107-023-01950-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 204 2023 1-2 19 04 81-111
allfieldsSound	10.1007/s10107-023-01950-8 doi (DE-627)SPR054780144 (SPR)s10107-023-01950-8-e DE-627 ger DE-627 rakwb eng Guenin, Bertrand verfasserin (orcid)0000-0001-8661-6196 aut Small separations in pinch-graphic matroids 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids. Binary matroids (dpeaa)DE-He213 Signed-graphs (dpeaa)DE-He213 Grafts (dpeaa)DE-He213 Algorithms (dpeaa)DE-He213 Complexity (dpeaa)DE-He213 Heo, Cheolwon aut Enthalten in Mathematical programming Berlin : Springer, 1971 204(2023), 1-2 vom: 19. Apr., Seite 81-111 (DE-627)25491179X (DE-600)1463397-8 1436-4646 nnns volume:204 year:2023 number:1-2 day:19 month:04 pages:81-111 https://dx.doi.org/10.1007/s10107-023-01950-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 204 2023 1-2 19 04 81-111
language	English
source	Enthalten in Mathematical programming 204(2023), 1-2 vom: 19. Apr., Seite 81-111 volume:204 year:2023 number:1-2 day:19 month:04 pages:81-111
sourceStr	Enthalten in Mathematical programming 204(2023), 1-2 vom: 19. Apr., Seite 81-111 volume:204 year:2023 number:1-2 day:19 month:04 pages:81-111
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Binary matroids Signed-graphs Grafts Algorithms Complexity
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container_title	Mathematical programming
authorswithroles_txt_mv	Guenin, Bertrand @@aut@@ Heo, Cheolwon @@aut@@
publishDateDaySort_date	2023-04-19T00:00:00Z
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language_de	englisch
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author	Guenin, Bertrand
spellingShingle	Guenin, Bertrand misc Binary matroids misc Signed-graphs misc Grafts misc Algorithms misc Complexity Small separations in pinch-graphic matroids
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topic_title	Small separations in pinch-graphic matroids Binary matroids (dpeaa)DE-He213 Signed-graphs (dpeaa)DE-He213 Grafts (dpeaa)DE-He213 Algorithms (dpeaa)DE-He213 Complexity (dpeaa)DE-He213
topic	misc Binary matroids misc Signed-graphs misc Grafts misc Algorithms misc Complexity
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title	Small separations in pinch-graphic matroids
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title_full	Small separations in pinch-graphic matroids
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title_sort	small separations in pinch-graphic matroids
title_auth	Small separations in pinch-graphic matroids
abstract	Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids. © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids. © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids. © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	Small separations in pinch-graphic matroids
url	https://dx.doi.org/10.1007/s10107-023-01950-8
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author2	Heo, Cheolwon
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doi_str	10.1007/s10107-023-01950-8
up_date	2024-07-04T02:59:33.715Z
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