Mixed graph edge coloring

Source Information
June 2009, Volume309(Issue12) Page4027To4036

Abstract

We are interested in coloring the edges of a mixed graph, i.e., a graph containing unoriented and oriented edges. This problem is related to a communication problem in job-shop scheduling systems. In this paper we give general bounds on the number of required colors and analyze the complexity status of this problem. In particular, we provide N P -completeness results for the case of outerplanar graphs, as well as for 3-regular bipartite graphs (even when only 3 colors are allowed, or when 5 colors are allowed and the graph is fully oriented). Special cases admitting polynomial-time solutions are also discussed.

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doi: 10.1016/j.disc.2008.11.033