The Mutual Exclusion Scheduling Problem for Permutation and Comparability Graphs
نویسنده
چکیده
In this paper, we consider the mutual exclusion scheduling problem for comparability graphs. Given an undirected graph G and a xed constant m, the problem is to nd a minimum coloring of G such that each color is used at most m times. The complexity of this problem for comparability graphs was mentioned as an open problem by M ohring (1985) and for permutation graphs (a subclass of comparability graphs) as an open problem by Lonc (1991). We prove that this problem is already NP-complete for permutation graphs and for each xed constant m 6.
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