# Discrete Mathematics & Theoretical Computer Science

## Volume 4 n° 2 (2001), pp. 109-122

author: | Chính T. Hoàng and Van Bang Le |
---|---|

title: | P-Colorings and _{4}P-Bipartite Graphs_{4} |

keywords: | Perfect graph, the Strong Perfect Graph Conjectrue, graph partition, cograph, NP-completeness |

abstract: | A vertex partition of a graph into disjoint subsets Vs is said to be a
_{i}P-free coloring if each color class
_{4}V induces a subgraph without chordless path
on four vertices (denoted by _{i}P). Examples of
_{4}P-free 2-colorable graphs (also called
_{4}P-bipartite graphs) include parity graphs and
graphs with ``few'' _{4}Ps like
_{4}P-reducible and
_{4}P-sparse graphs. We prove that, given
_{4}k≥2, is NP-complete even for
comparability graphs, and for P-Free
_{4}k-ColorabilityP-free
graphs. We then discuss the recognition, perfection and the Strong
Perfect Graph Conjecture (SPGC) for
_{5}P-bipartite graphs with special
_{4}P-structure. In particular, we show that the
SPGC is true for _{4}P-bipartite graphs with one
_{4}P-free color class meeting every
_{3}P at a midpoint.
_{4}If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

reference: | Chính T. Hoàng and Van Bang Le (2001),
P-Colorings and _{4}P-Bipartite Graphs,
_{4}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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