In this paper we consider a problem of graph P-coloring consisting in partitioning the vertex set of a graph such that each of the resulting sets induces a graph in a given additive, hereditary class of graphs P. We focus on partitions generated by the greedy algorithm. In particular, we show that given a graph G andanintegerk deciding if the greedy algorithm outputs a P-coloring with a least k colors is NP-complete for an infinite number of classes P. On the other hand we get a polynomial-time certifying algorithm if k is fixed and the family of minimal forbidden graphs defining the class P is finite. We also prove coNP-completeness of the problem of deciding whether for a given graph G the difference between the largest number of colors used by the greedy algorithm and the minimum number of colors required in any P-coloring of G is bounded by a given constant. A new Brooks-type bound on the largest number of colors used by the greedy P-coloring algorithm is given.
CITATION STYLE
Borowiecki, P. (2017). On computational aspects of greedy partitioning of graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10336 LNCS, pp. 34–46). Springer Verlag. https://doi.org/10.1007/978-3-319-59605-1_4
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