P_4-Colorings and P_4-Bipartite Graphs - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2001

P_4-Colorings and P_4-Bipartite Graphs


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.
Fichier principal
Vignette du fichier
dm040204.pdf (114.57 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00958951 , version 1 (13-03-2014)



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


62 View
822 Download



Gmail Facebook Twitter LinkedIn More