The edge chromatic number of a directed-mixed multigraph

Authors:
Leonid S. Mel'nikov;Vadim G. Vizing
Affiliations:
Institute of Mathematics, Siberian Branch of RAS, Novosibirsk 630090, Russia;Department of Applied Mathematics, Odessa's State Food Technology Academy, Kanatnaja str. 112, Odessa 270039, Ukraine
Venue:
Journal of Graph Theory
Year:
1999

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Abstract

We consider colorings of the directed and undirected edges of a mixed multigraph G by an ordered set of colors. We color each undirected edge in one color and each directed edge in two colors, such that the color of the first half of a directed edge is smaller than the color of the second half. The colors used at the same vertex are all different. A bound for the minimum number of colors needed for such colorings is obtained. In the case where G has only directed edges, we provide a polynomal algorithm for coloring G with a minimum number of colors. An unsolved problem is formulated. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 267–273, 1999 Both authors carried out this work during their visit to Odensse University in March, 1995.