Mixed graph edge coloring

Hanna Furmańczyk, Adrian Kosowski, Bernard Ries, Paweł Żyliński
2009 Discrete Mathematics  
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 Pcompleteness 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
more » ... are allowed and the graph is fully oriented). Special cases admitting polynomial-time solutions are also discussed.
doi:10.1016/j.disc.2008.11.033 fatcat:cxei7a7u6jf7raoeblkjpm3eiu