Discrete Mathematics & Theoretical Computer Science
| author: | Chính T. Hoàng and Van Bang Le |
|---|---|
| title: | P4-Colorings and P4-Bipartite Graphs |
| keywords: | Perfect graph, the Strong Perfect Graph Conjectrue, graph partition, cograph, NP-completeness |
| abstract: | A vertex partition of a graph into disjoint subsets Vis is said to be a
P4-free coloring if each color class
Vi induces a subgraph without chordless path
on four vertices (denoted by P4). Examples of
P4-free 2-colorable graphs (also called
P4-bipartite graphs) include parity graphs and
graphs with ``few'' P4s like
P4-reducible and
P4-sparse graphs. We prove that, given
k≥2, P4-Free
k-Colorability is NP-complete even for
comparability graphs, and for P5-free
graphs. We then discuss the recognition, perfection and the Strong
Perfect Graph Conjecture (SPGC) for
P4-bipartite graphs with special
P4-structure. In particular, we show that the
SPGC is true for P4-bipartite graphs with one
P3-free color class meeting every
P4 at a midpoint.
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| reference: | Chính T. Hoàng and Van Bang Le (2001), P4-Colorings and P4-Bipartite Graphs, Discrete Mathematics and Theoretical Computer Science 4, pp. 109-122 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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| pdf-source: | dm040204.pdf (131 K) |
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