A subcoloring is a vertex coloring of a graph in which every color class induces a disjoint union of cliques. We derive a number of results on the combinatorics, the algorithmics, and the complexity of subcolorings.
On the negative side, we prove that 2-subcoloring is NP-hard for comparability graphs, and that 3-subcoloring is NP-hard for AT-free graphs and for complements of planar graphs. On the positive side, we derive polynomial time algorithms for 2-subcoloring of complements of planar graphs, and for r-subcoloring of interval and of permutation graphs. Moreover, we prove asymptotically best possible upper bounds on the subchromatic number of interval graphs, chordal graphs, and permutation graphs in terms of the number of vertices.
AMS Subject Classifications: 05C15, 05C85, 05C17.
Keywords: graph coloring, subcoloring, special graph classes, polynomial time algorithm, computational complexity.
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1.Faculty of Mathematical Sciences University of Twente 7500 AE Enschede, The Netherlands e-mail: firstname.lastname@example.orgNL
2.Department of Applied Mathematics and Institute of Theoretical Computer Science (ITI) Faculty of Mathematics and Physics Charles University 118 00 Prague, Czech Republic e-mail: email@example.comCZ
3.Heinz Nixdorf Institut University of Paderborn D-33102 Paderborn, Germany e-mail: firstname.lastname@example.orgDE
4.Faculty of Mathematical Sciences University of Twente 7500 AE Enschede, The Netherlands e-mail: email@example.comNL