Rainbow connectivity of Moore cages of girth 6
Let be an edge-colored graph. A path of is said to be rainbow if no two edges of have the same color. An edge-coloring of is a rainbow-coloring if for any two distinct vertices and of there are at least internally vertex-disjoint rainbow -paths. The rainbow-connectivity of a graph is the minimum int...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/123591 |
| Acceso en línea: | https://hdl.handle.net/2117/123591 https://dx.doi.org/10.1016/j.dam.2018.04.020 |
| Access Level: | acceso abierto |
| Palabra clave: | Combinatorial analysis Rainbow coloring Rainbow connectivity Cages Combinacions (Matemàtica) Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Sumario: | Let be an edge-colored graph. A path of is said to be rainbow if no two edges of have the same color. An edge-coloring of is a rainbow-coloring if for any two distinct vertices and of there are at least internally vertex-disjoint rainbow -paths. The rainbow-connectivity of a graph is the minimum integer such that there exists a rainbow -coloring using colors. A -cage is a -regular graph of girth and minimum number of vertices denoted . In this paper we focus on . It is known that and when the -cage is called a Moore cage. In this paper we prove that the rainbow -connectivity of a Moore -cage satisfies that . It is also proved that the rainbow 3-connectivity of the Heawood graph is 6 or 7. |
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