Skip to Main content Skip to Navigation
Journal articles

P_4-Colorings and P_4-Bipartite Graphs

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [32 references]  Display  Hide  Download
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s Connect in order to contact the contributor
Submitted on : Thursday, March 13, 2014 - 4:51:53 PM
Last modification on : Friday, November 23, 2018 - 3:38:02 PM
Long-term archiving on: : Friday, June 13, 2014 - 12:03:47 PM


Files produced by the author(s)




Chinh T. Hoàng, van Bang Le. P_4-Colorings and P_4-Bipartite Graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2001, Vol. 4 no. 2 (2), pp.109-122. ⟨10.46298/dmtcs.272⟩. ⟨hal-00958951⟩



Record views


Files downloads