Discrete Mathematics & Theoretical Computer Science |

- 1 Department of Physics and Computer Science [Waterloo]

A vertex partition of a graph into disjoint subsets V_is 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_4s like P_4-reducible and P_4-sparse graphs. We prove that, given k≥ 2, \emphP_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.

Source: HAL:hal-00958951v1

Volume: Vol. 4 no. 2

Published on: January 1, 2001

Imported on: March 26, 2015

Keywords: Perfect graph,the Strong Perfect Graph Conjectrue,graph partition,cograph,NP-completeness,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Funding:

- Source : OpenAIRE Graph
- Funder: Natural Sciences and Engineering Research Council of Canada

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