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 and an integer k 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.
Authors
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1007/978-3-319-59605-1_4
- Category
- Aktywność konferencyjna
- Type
- publikacja w wydawnictwie zbiorowym recenzowanym (także w materiałach konferencyjnych)
- Language
- angielski
- Publication year
- 2017
