Integral and rational graphs in the plane

We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erdös. We also mention some related problems.

Gespeichert in:

Autor*in:	Solymosi, Jozsef [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	DISTANCE Integer distances Integral graphs LINE POINTS Rational graphs

Anmerkung:	Last seen: 25.10.2024

Übergeordnetes Werk:	Enthalten in: Graphs and combinatorics - Tokyo : Springer-Verl. Tokyo, 1985, Volume 40(2024), Issue 6, Article no. 107
Übergeordnetes Werk:	volume:40 ; year:2024 ; number:6 ; elocationid:107

Links:	Full Text at Publisher

DOI / URN:	10.1007/s00373-024-02841-1

Katalog-ID:	1906885656

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allfields	10.1007/s00373-024-02841-1 doi (DE-627)1906885656 (DE-599)KXP1906885656 DE-627 ger DE-627 rda eng 52C10 51K05 05C10 msc Solymosi, Jozsef verfasserin aut Integral and rational graphs in the plane 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 25.10.2024 We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erdös. We also mention some related problems. DISTANCE Integer distances Integral graphs LINE POINTS Rational graphs Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 Volume 40(2024), Issue 6, Article no. 107 Online-Ressource (DE-627)30018381X (DE-600)1481435-3 (DE-576)107930668 1435-5914 nnns volume:40 year:2024 number:6 elocationid:107 https://doi.org/10.1007/s00373-024-02841-1 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_72 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 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_4598 GBV_ILN_4700 AR 40 2024 6 107 Volume 40(2024), Issue 6, Article no. 107 2088 01 DE-Frei3c 4602563090 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This article was funded by Hungarian Scientific Research Fund (Grant no. 133819), a joint grant of the Simons Foundation and the Mathematisches Forschungsinstitut Oberwolfach, Natural Sciences and Engineering Research Council of Canada. l01 25-10-24 2088 01 DE-Frei3c 00 (DE-627)1295066556 AMS:52 [MSC]Convex and discrete geometry 2088 01 DE-Frei3c 00 (DE-627)129544187X AMS:51 [MSC]Geometry 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 [MSC]Combinatorics
spelling	10.1007/s00373-024-02841-1 doi (DE-627)1906885656 (DE-599)KXP1906885656 DE-627 ger DE-627 rda eng 52C10 51K05 05C10 msc Solymosi, Jozsef verfasserin aut Integral and rational graphs in the plane 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 25.10.2024 We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erdös. We also mention some related problems. DISTANCE Integer distances Integral graphs LINE POINTS Rational graphs Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 Volume 40(2024), Issue 6, Article no. 107 Online-Ressource (DE-627)30018381X (DE-600)1481435-3 (DE-576)107930668 1435-5914 nnns volume:40 year:2024 number:6 elocationid:107 https://doi.org/10.1007/s00373-024-02841-1 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_72 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 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_4598 GBV_ILN_4700 AR 40 2024 6 107 Volume 40(2024), Issue 6, Article no. 107 2088 01 DE-Frei3c 4602563090 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This article was funded by Hungarian Scientific Research Fund (Grant no. 133819), a joint grant of the Simons Foundation and the Mathematisches Forschungsinstitut Oberwolfach, Natural Sciences and Engineering Research Council of Canada. l01 25-10-24 2088 01 DE-Frei3c 00 (DE-627)1295066556 AMS:52 [MSC]Convex and discrete geometry 2088 01 DE-Frei3c 00 (DE-627)129544187X AMS:51 [MSC]Geometry 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 [MSC]Combinatorics
allfields_unstemmed	10.1007/s00373-024-02841-1 doi (DE-627)1906885656 (DE-599)KXP1906885656 DE-627 ger DE-627 rda eng 52C10 51K05 05C10 msc Solymosi, Jozsef verfasserin aut Integral and rational graphs in the plane 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 25.10.2024 We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erdös. We also mention some related problems. DISTANCE Integer distances Integral graphs LINE POINTS Rational graphs Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 Volume 40(2024), Issue 6, Article no. 107 Online-Ressource (DE-627)30018381X (DE-600)1481435-3 (DE-576)107930668 1435-5914 nnns volume:40 year:2024 number:6 elocationid:107 https://doi.org/10.1007/s00373-024-02841-1 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_72 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 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_4598 GBV_ILN_4700 AR 40 2024 6 107 Volume 40(2024), Issue 6, Article no. 107 2088 01 DE-Frei3c 4602563090 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This article was funded by Hungarian Scientific Research Fund (Grant no. 133819), a joint grant of the Simons Foundation and the Mathematisches Forschungsinstitut Oberwolfach, Natural Sciences and Engineering Research Council of Canada. l01 25-10-24 2088 01 DE-Frei3c 00 (DE-627)1295066556 AMS:52 [MSC]Convex and discrete geometry 2088 01 DE-Frei3c 00 (DE-627)129544187X AMS:51 [MSC]Geometry 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 [MSC]Combinatorics
allfieldsGer	10.1007/s00373-024-02841-1 doi (DE-627)1906885656 (DE-599)KXP1906885656 DE-627 ger DE-627 rda eng 52C10 51K05 05C10 msc Solymosi, Jozsef verfasserin aut Integral and rational graphs in the plane 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 25.10.2024 We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erdös. We also mention some related problems. DISTANCE Integer distances Integral graphs LINE POINTS Rational graphs Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 Volume 40(2024), Issue 6, Article no. 107 Online-Ressource (DE-627)30018381X (DE-600)1481435-3 (DE-576)107930668 1435-5914 nnns volume:40 year:2024 number:6 elocationid:107 https://doi.org/10.1007/s00373-024-02841-1 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_72 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 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_4598 GBV_ILN_4700 AR 40 2024 6 107 Volume 40(2024), Issue 6, Article no. 107 2088 01 DE-Frei3c 4602563090 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This article was funded by Hungarian Scientific Research Fund (Grant no. 133819), a joint grant of the Simons Foundation and the Mathematisches Forschungsinstitut Oberwolfach, Natural Sciences and Engineering Research Council of Canada. l01 25-10-24 2088 01 DE-Frei3c 00 (DE-627)1295066556 AMS:52 [MSC]Convex and discrete geometry 2088 01 DE-Frei3c 00 (DE-627)129544187X AMS:51 [MSC]Geometry 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 [MSC]Combinatorics
allfieldsSound	10.1007/s00373-024-02841-1 doi (DE-627)1906885656 (DE-599)KXP1906885656 DE-627 ger DE-627 rda eng 52C10 51K05 05C10 msc Solymosi, Jozsef verfasserin aut Integral and rational graphs in the plane 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 25.10.2024 We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erdös. We also mention some related problems. DISTANCE Integer distances Integral graphs LINE POINTS Rational graphs Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 Volume 40(2024), Issue 6, Article no. 107 Online-Ressource (DE-627)30018381X (DE-600)1481435-3 (DE-576)107930668 1435-5914 nnns volume:40 year:2024 number:6 elocationid:107 https://doi.org/10.1007/s00373-024-02841-1 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_72 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 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_4598 GBV_ILN_4700 AR 40 2024 6 107 Volume 40(2024), Issue 6, Article no. 107 2088 01 DE-Frei3c 4602563090 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This article was funded by Hungarian Scientific Research Fund (Grant no. 133819), a joint grant of the Simons Foundation and the Mathematisches Forschungsinstitut Oberwolfach, Natural Sciences and Engineering Research Council of Canada. l01 25-10-24 2088 01 DE-Frei3c 00 (DE-627)1295066556 AMS:52 [MSC]Convex and discrete geometry 2088 01 DE-Frei3c 00 (DE-627)129544187X AMS:51 [MSC]Geometry 2088 01 DE-Frei3c 00 (DE-627)1294696033 AMS:05 [MSC]Combinatorics
language	English
source	Enthalten in Graphs and combinatorics Volume 40(2024), Issue 6, Article no. 107 volume:40 year:2024 number:6 elocationid:107
sourceStr	Enthalten in Graphs and combinatorics Volume 40(2024), Issue 6, Article no. 107 volume:40 year:2024 number:6 elocationid:107
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topic_title	52C10 51K05 05C10 msc Integral and rational graphs in the plane DISTANCE Integer distances Integral graphs LINE POINTS Rational graphs
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title_full	Integral and rational graphs in the plane
author_sort	Solymosi, Jozsef
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class_local_iln	2088:[MSC]Convex and discrete geometry DE-Frei3c:[MSC]Convex and discrete geometry 2088:[MSC]Geometry DE-Frei3c:[MSC]Geometry 2088:[MSC]Combinatorics DE-Frei3c:[MSC]Combinatorics
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title_sort	integral and rational graphs in the plane
title_auth	Integral and rational graphs in the plane
abstract	We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erdös. We also mention some related problems. Last seen: 25.10.2024
abstractGer	We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erdös. We also mention some related problems. Last seen: 25.10.2024
abstract_unstemmed	We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erdös. We also mention some related problems. Last seen: 25.10.2024
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container_issue	6
title_short	Integral and rational graphs in the plane
url	https://doi.org/10.1007/s00373-024-02841-1
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doi_str	10.1007/s00373-024-02841-1
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up_date	2024-10-26T05:42:12.532Z
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