Discrete Mathematics & Theoretical Computer Science, Vol 4, No 2 (2001)

Font Size:  Small  Medium  Large
DMTCS vol 4 no 2 (2001), pp. 109-122

Discrete Mathematics & Theoretical Computer Science


Volume 4 n° 2 (2001), pp. 109-122

author:Chính T. Hoàng and Van Bang Le
title:P4-Colorings and P4-Bipartite Graphs
keywords:Perfect graph, the Strong Perfect Graph Conjectrue, graph partition, cograph, NP-completeness
abstract:A vertex partition of a graph into disjoint subsets Vis is said to be a P4-free coloring if each color class Vi induces a subgraph without chordless path on four vertices (denoted by P4). Examples of P4-free 2-colorable graphs (also called P4-bipartite graphs) include parity graphs and graphs with ``few'' P4s like P4-reducible and P4-sparse graphs. We prove that, given k≥2, P4-Free k-Colorability is NP-complete even for comparability graphs, and for P5-free graphs. We then discuss the recognition, perfection and the Strong Perfect Graph Conjecture (SPGC) for P4-bipartite graphs with special P4-structure. In particular, we show that the SPGC is true for P4-bipartite graphs with one P3-free color class meeting every P4 at a midpoint.

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), P4-Colorings and P4-Bipartite Graphs, Discrete Mathematics and Theoretical Computer Science 4, pp. 109-122
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
ps.gz-source:dm040204.ps.gz (47)
ps-source:dm040204.ps (148)
pdf-source:dm040204.pdf (131 K)

The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.

Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.

Automatically produced on Sun Jun 20 23:02:11 CEST 2004 by gustedt