P 4-Colorings and P 4-Bipartite Graphs
A vertex partition of a graph into disjoint subsets V i s is said to be a P 4-free coloring if each color class V i induces a subgraph without chordless path on four vertices (denoted by P 4). Examples of P 4-free 2-colorable graphs (also called P 4-bipartite graphs) include parity...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2001-12-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/140 |
| Summary: | A vertex partition of a graph into disjoint subsets V i s is said to be a P 4-free coloring if each color class V i induces a subgraph without chordless path on four vertices (denoted by P 4). Examples of P 4-free 2-colorable graphs (also called P 4-bipartite graphs) include parity graphs and graphs with ``few'' P 4 s like P 4-reducible and P 4-sparse graphs. We prove that, given k≥2, P 4-Free k-Colorability is NP-complete even for comparability graphs, and for P 5-free graphs. We then discuss the recognition, perfection and the Strong Perfect Graph Conjecture (SPGC) for P 4-bipartite graphs with special P 4-structure. In particular, we show that the SPGC is true for P 4-bipartite graphs with one P 3-free color class meeting every P 4 at a midpoint. |
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| ISSN: | 1462-7264 1365-8050 |