On the [r, s, t]-coloring of the square of cylindrical grids
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| Názov: | On the [r, s, t]-coloring of the square of cylindrical grids |
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| Autori: | Effantin, Brice |
| Prispievatelia: | JARDIN, Nicolas |
| Zdroj: | Discrete Mathematics Letters, Vol 15, Pp 15-22 (2025) |
| Informácie o vydavateľovi: | Shahin Digital Publisher, 2025. |
| Rok vydania: | 2025 |
| Predmety: | [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], total coloring, vertex coloring, QA1-939, cartesian product, edge coloring, Mathematics |
| Popis: | The [r,s,t]-coloring is a generalization of the classical vertex, edge, and total colorings, where two vertices, two edges, and a vertex and its incident edges have colors distant by at least r, s and t, respectively. The square of a graph G is a graph obtained from G by adding an edge between two vertices at a distance at most 2 in G. A cylindrical grid is equivalent to the Cartesian product of a path and a cycle. In this article, colorings for the square of cylindrical grids are discussed. It is shown that such graphs are class one graphs (according to Vizing’s theorem). For the [r,s,t]-coloring of these graphs, particular values of r, s and t are presented, for which the minimum number of colors needed in an [r,s,t]-coloring is determined. |
| Druh dokumentu: | Article |
| Popis súboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 2664-2557 |
| DOI: | 10.47443/dml.2024.148 |
| Prístupová URL adresa: | https://doaj.org/article/0e0afada48ac4b7c8c541dca969fe876 |
| Prístupové číslo: | edsair.doi.dedup.....f2ca4a9d2a68ca154cfa2e2a0a366bad |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | The [r,s,t]-coloring is a generalization of the classical vertex, edge, and total colorings, where two vertices, two edges, and a vertex and its incident edges have colors distant by at least r, s and t, respectively. The square of a graph G is a graph obtained from G by adding an edge between two vertices at a distance at most 2 in G. A cylindrical grid is equivalent to the Cartesian product of a path and a cycle. In this article, colorings for the square of cylindrical grids are discussed. It is shown that such graphs are class one graphs (according to Vizing’s theorem). For the [r,s,t]-coloring of these graphs, particular values of r, s and t are presented, for which the minimum number of colors needed in an [r,s,t]-coloring is determined. |
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| ISSN: | 26642557 |
| DOI: | 10.47443/dml.2024.148 |