A Vizing-type theorem for matching forests

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3 Citations (Scopus)

Abstract

A well-known Theorem of Vizing states that one can colour the edges of a graph by Δ + α colours, such that edges of the same colour form a matching. Here, Δ denotes the maximum degree of a vertex, and α the maximum multiplicity of an edge in the graph. An analogue of this Theorem for directed graphs was proved by Frank. It states that one can colour the arcs of a digraph by Δ + α colours, such that arcs of the same colour form a branching. For a digraph, A denotes the maximum indegree of a vertex, and a the maximum multiplicity of an arc. We prove a common generalization of the above two theorems concerning the colouring of mixed graphs (these are graphs having both directed and undirected edges) in such a way that edges of the same colour form a matching forest.

Original languageEnglish
Pages (from-to)211-216
Number of pages6
JournalDiscrete Mathematics
Volume260
Issue number1-3
DOIs
Publication statusPublished - 6 Jan 2003

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