Faculté des sciences économiques et sociales

Mixed graph edge coloring

Furmańczyk, Hanna ; Kosowski, Adrian ; Ries, Bernard ; Żyliński, Paweł

In: Discrete Mathematics, 2009, vol. 309, no. 12, p. 4027-4036

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 NP-completeness results for the case of outerplanar... More

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    Summary
    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 NP-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.