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Title:
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Rainbow connectivity of Moore cages of girth 6
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Author:
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Balbuena Martínez, Maria Camino Teófila; Fresán Figueroa, J.; González Moreno, Diego; Olsen, Mika
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Other authors:
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Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
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Abstract:
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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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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
-Combinatorial analysis
-Rainbow coloring
-Rainbow connectivity
-Cages
-Combinacions (Matemàtica)
-Classificació AMS::05 Combinatorics::05C Graph theory |
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Rights:
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Document type:
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Article - Submitted version
Article |
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