# A vizing-type theorem for matching forests

J.C.M. Keijsper

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### Abstract

A well known Theorem of Vizing states that one can colour the edges of a graph by $\Delta +\alpha$ colours, such that edges of the same colour form a matching. Here, $\Delta$ denotes the maximum degree of a vertex, and $\alpha$ 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 $\Delta +\alpha$ colours, such that arcs of the same colour form a branching. For a digraph, $\Delta$ denotes the maximum indegree of a vertex, and $\alpha$ the maximum multiplicity of an arc.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics Published - 2000

### Publication series

Name Department of Applied Mathematics, University of Twente 1517 0169-2690

• MSC-05C70
• IR-65705
• MSC-05C15
• EWI-3337

### Cite this

Keijsper, J. C. M. (2000). A vizing-type theorem for matching forests. Enschede: University of Twente, Department of Applied Mathematics.