TY - JOUR

T1 - A Vizing-type theorem for matching forests

AU - Keijsper, Judith

PY - 2003/1/6

Y1 - 2003/1/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037421161&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(02)00671-4

DO - 10.1016/S0012-365X(02)00671-4

M3 - Article

VL - 260

SP - 211

EP - 216

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -