Annulus Graphs in $$\mathbb R^d$$
Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Lichev, Lyuben [verfasserIn] Mihaylov, Tsvetomir [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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| Anmerkung: |
© Crown 2024 |
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| Übergeordnetes Werk: |
Enthalten in: Discrete & computational geometry - Springer US, 1986, 72(2024), 1 vom: 16. Mai, Seite 379-401 |
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| Übergeordnetes Werk: |
volume:72 ; year:2024 ; number:1 ; day:16 ; month:05 ; pages:379-401 |
| Links: |
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| DOI / URN: |
10.1007/s00454-024-00649-7 |
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| Katalog-ID: |
SPR056085117 |
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| 520 | |a Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. Moreover, as a step towards a better understanding of the structure of $$\mathcal A_d(R_1,R_2)$$, we show that $$\sup _{G\in \mathcal A_d(R_1,R_2)} \chi (G)/\omega (G)$$ is given by $$\exp (O(d))$$ for all $$R_1,R_2$$ satisfying $$R_2\ge R_1 > 0$$ and also $$\exp (\Omega (d))$$ if moreover $$R_2/R_1\ge 1.2$$. | ||
| 650 | 4 | |a Annulus graph |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Geometric embedding |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Clique number |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Chromatic number |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Mihaylov, Tsvetomir |e verfasserin |0 (orcid)0000-0002-7363-7139 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Discrete & computational geometry |d Springer US, 1986 |g 72(2024), 1 vom: 16. Mai, Seite 379-401 |w (DE-627)253722330 |w (DE-600)1459007-4 |x 1432-0444 |7 nnns |
| 773 | 1 | 8 | |g volume:72 |g year:2024 |g number:1 |g day:16 |g month:05 |g pages:379-401 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00454-024-00649-7 |m X:SPRINGER |x Resolving-System |z kostenfrei |3 Volltext |
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10.1007/s00454-024-00649-7 doi (DE-627)SPR056085117 (SPR)s00454-024-00649-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Lichev, Lyuben verfasserin aut Annulus Graphs in $$\mathbb R^d$$ 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Crown 2024 Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. Moreover, as a step towards a better understanding of the structure of $$\mathcal A_d(R_1,R_2)$$, we show that $$\sup _{G\in \mathcal A_d(R_1,R_2)} \chi (G)/\omega (G)$$ is given by $$\exp (O(d))$$ for all $$R_1,R_2$$ satisfying $$R_2\ge R_1 > 0$$ and also $$\exp (\Omega (d))$$ if moreover $$R_2/R_1\ge 1.2$$. Annulus graph (dpeaa)DE-He213 Geometric embedding (dpeaa)DE-He213 Clique number (dpeaa)DE-He213 Chromatic number (dpeaa)DE-He213 Mihaylov, Tsvetomir verfasserin (orcid)0000-0002-7363-7139 aut Enthalten in Discrete & computational geometry Springer US, 1986 72(2024), 1 vom: 16. Mai, Seite 379-401 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:72 year:2024 number:1 day:16 month:05 pages:379-401 https://dx.doi.org/10.1007/s00454-024-00649-7 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_101 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_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_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_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 31.59 VZ 31.12 VZ 31.76 VZ AR 72 2024 1 16 05 379-401 |
| spelling |
10.1007/s00454-024-00649-7 doi (DE-627)SPR056085117 (SPR)s00454-024-00649-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Lichev, Lyuben verfasserin aut Annulus Graphs in $$\mathbb R^d$$ 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Crown 2024 Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. Moreover, as a step towards a better understanding of the structure of $$\mathcal A_d(R_1,R_2)$$, we show that $$\sup _{G\in \mathcal A_d(R_1,R_2)} \chi (G)/\omega (G)$$ is given by $$\exp (O(d))$$ for all $$R_1,R_2$$ satisfying $$R_2\ge R_1 > 0$$ and also $$\exp (\Omega (d))$$ if moreover $$R_2/R_1\ge 1.2$$. Annulus graph (dpeaa)DE-He213 Geometric embedding (dpeaa)DE-He213 Clique number (dpeaa)DE-He213 Chromatic number (dpeaa)DE-He213 Mihaylov, Tsvetomir verfasserin (orcid)0000-0002-7363-7139 aut Enthalten in Discrete & computational geometry Springer US, 1986 72(2024), 1 vom: 16. Mai, Seite 379-401 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:72 year:2024 number:1 day:16 month:05 pages:379-401 https://dx.doi.org/10.1007/s00454-024-00649-7 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_101 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_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_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_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 31.59 VZ 31.12 VZ 31.76 VZ AR 72 2024 1 16 05 379-401 |
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10.1007/s00454-024-00649-7 doi (DE-627)SPR056085117 (SPR)s00454-024-00649-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Lichev, Lyuben verfasserin aut Annulus Graphs in $$\mathbb R^d$$ 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Crown 2024 Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. Moreover, as a step towards a better understanding of the structure of $$\mathcal A_d(R_1,R_2)$$, we show that $$\sup _{G\in \mathcal A_d(R_1,R_2)} \chi (G)/\omega (G)$$ is given by $$\exp (O(d))$$ for all $$R_1,R_2$$ satisfying $$R_2\ge R_1 > 0$$ and also $$\exp (\Omega (d))$$ if moreover $$R_2/R_1\ge 1.2$$. Annulus graph (dpeaa)DE-He213 Geometric embedding (dpeaa)DE-He213 Clique number (dpeaa)DE-He213 Chromatic number (dpeaa)DE-He213 Mihaylov, Tsvetomir verfasserin (orcid)0000-0002-7363-7139 aut Enthalten in Discrete & computational geometry Springer US, 1986 72(2024), 1 vom: 16. Mai, Seite 379-401 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:72 year:2024 number:1 day:16 month:05 pages:379-401 https://dx.doi.org/10.1007/s00454-024-00649-7 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_101 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_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_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_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 31.59 VZ 31.12 VZ 31.76 VZ AR 72 2024 1 16 05 379-401 |
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10.1007/s00454-024-00649-7 doi (DE-627)SPR056085117 (SPR)s00454-024-00649-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Lichev, Lyuben verfasserin aut Annulus Graphs in $$\mathbb R^d$$ 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Crown 2024 Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. Moreover, as a step towards a better understanding of the structure of $$\mathcal A_d(R_1,R_2)$$, we show that $$\sup _{G\in \mathcal A_d(R_1,R_2)} \chi (G)/\omega (G)$$ is given by $$\exp (O(d))$$ for all $$R_1,R_2$$ satisfying $$R_2\ge R_1 > 0$$ and also $$\exp (\Omega (d))$$ if moreover $$R_2/R_1\ge 1.2$$. Annulus graph (dpeaa)DE-He213 Geometric embedding (dpeaa)DE-He213 Clique number (dpeaa)DE-He213 Chromatic number (dpeaa)DE-He213 Mihaylov, Tsvetomir verfasserin (orcid)0000-0002-7363-7139 aut Enthalten in Discrete & computational geometry Springer US, 1986 72(2024), 1 vom: 16. Mai, Seite 379-401 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:72 year:2024 number:1 day:16 month:05 pages:379-401 https://dx.doi.org/10.1007/s00454-024-00649-7 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_101 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_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_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_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 31.59 VZ 31.12 VZ 31.76 VZ AR 72 2024 1 16 05 379-401 |
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10.1007/s00454-024-00649-7 doi (DE-627)SPR056085117 (SPR)s00454-024-00649-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Lichev, Lyuben verfasserin aut Annulus Graphs in $$\mathbb R^d$$ 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Crown 2024 Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. Moreover, as a step towards a better understanding of the structure of $$\mathcal A_d(R_1,R_2)$$, we show that $$\sup _{G\in \mathcal A_d(R_1,R_2)} \chi (G)/\omega (G)$$ is given by $$\exp (O(d))$$ for all $$R_1,R_2$$ satisfying $$R_2\ge R_1 > 0$$ and also $$\exp (\Omega (d))$$ if moreover $$R_2/R_1\ge 1.2$$. Annulus graph (dpeaa)DE-He213 Geometric embedding (dpeaa)DE-He213 Clique number (dpeaa)DE-He213 Chromatic number (dpeaa)DE-He213 Mihaylov, Tsvetomir verfasserin (orcid)0000-0002-7363-7139 aut Enthalten in Discrete & computational geometry Springer US, 1986 72(2024), 1 vom: 16. Mai, Seite 379-401 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:72 year:2024 number:1 day:16 month:05 pages:379-401 https://dx.doi.org/10.1007/s00454-024-00649-7 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_101 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_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_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_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 31.59 VZ 31.12 VZ 31.76 VZ AR 72 2024 1 16 05 379-401 |
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Enthalten in Discrete & computational geometry 72(2024), 1 vom: 16. Mai, Seite 379-401 volume:72 year:2024 number:1 day:16 month:05 pages:379-401 |
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Enthalten in Discrete & computational geometry 72(2024), 1 vom: 16. Mai, Seite 379-401 volume:72 year:2024 number:1 day:16 month:05 pages:379-401 |
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In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. 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Lichev, Lyuben |
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Annulus Graphs in $$\mathbb R^d$$ |
| abstract |
Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. Moreover, as a step towards a better understanding of the structure of $$\mathcal A_d(R_1,R_2)$$, we show that $$\sup _{G\in \mathcal A_d(R_1,R_2)} \chi (G)/\omega (G)$$ is given by $$\exp (O(d))$$ for all $$R_1,R_2$$ satisfying $$R_2\ge R_1 > 0$$ and also $$\exp (\Omega (d))$$ if moreover $$R_2/R_1\ge 1.2$$. © Crown 2024 |
| abstractGer |
Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. Moreover, as a step towards a better understanding of the structure of $$\mathcal A_d(R_1,R_2)$$, we show that $$\sup _{G\in \mathcal A_d(R_1,R_2)} \chi (G)/\omega (G)$$ is given by $$\exp (O(d))$$ for all $$R_1,R_2$$ satisfying $$R_2\ge R_1 > 0$$ and also $$\exp (\Omega (d))$$ if moreover $$R_2/R_1\ge 1.2$$. © Crown 2024 |
| abstract_unstemmed |
Abstract A d-dimensional annulus graph with radii $$R_1$$ and $$R_2$$ (here $$R_2\ge R_1\ge 0$$) is a graph embeddable in $$\mathbb R^d$$ so that two vertices u and v form an edge if and only if their images in the embedding are at distance in the interval $$[R_1, R_2]$$. In this paper we show that the family $$\mathcal A_d(R_1,R_2)$$ of d-dimensional annulus graphs with radii $$R_1$$ and $$R_2$$ is uniquely characterised by $$R_2/R_1$$ when this ratio is sufficiently large. Moreover, as a step towards a better understanding of the structure of $$\mathcal A_d(R_1,R_2)$$, we show that $$\sup _{G\in \mathcal A_d(R_1,R_2)} \chi (G)/\omega (G)$$ is given by $$\exp (O(d))$$ for all $$R_1,R_2$$ satisfying $$R_2\ge R_1 > 0$$ and also $$\exp (\Omega (d))$$ if moreover $$R_2/R_1\ge 1.2$$. © Crown 2024 |
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1 |
| title_short |
Annulus Graphs in $$\mathbb R^d$$ |
| url |
https://dx.doi.org/10.1007/s00454-024-00649-7 |
| remote_bool |
true |
| author2 |
Mihaylov, Tsvetomir |
| author2Str |
Mihaylov, Tsvetomir |
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| doi_str |
10.1007/s00454-024-00649-7 |
| up_date |
2024-07-03T20:06:16.515Z |
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1803589702407684096 |
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| score |
7.4013834 |