Graph Subcolorings: Complexity and Algorithms

In a graph coloring, each color class induces a disjoint union of isolated vertices. A graph subcoloring generalizes this concept, since here each color class induces a disjoint union of complete graphs. Erd˝os and, independently, Albertson et al., proved that every graph of maximum degree at most 3 has a 2-subcoloring. We point out that this fact is best possible with respect to degree constraints by showing that the problem of recognizing 2-subcolorable graphs with maximum degree 4 is NP-complete, even when restricted to triangle-free planar graphs. Moreover, in general, for fixed k, recognizing k-subcolorable graphs is NP-complete on graphs with maximum degree at most k2. In contrast, we show that, for arbitrary k, k-subcolorability can be decided in linear time on graphs with bounded treewidth and on graphs with bounded cliquewidth (including cographs as a specific case). Key words. graph subcoloring, computational complexity, cograph, cliquewidth, treewidth AMS subject classi�...

• Type: Conference
• Year: 2001
• Where: WG
• Authors: Jirí Fiala, Klaus Jansen, Van Bang Le, Eike Seidel
• Keywords: Color Class, Disjoint Union, Maximum Degree, Theoretical Computer Science, WG 2001