Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published February 8, 2008 | public
Journal Article Open

A New Algorithm for On-line Coloring Bipartite Graphs

Abstract

We first show that for any bipartite graph $H$ with at most five vertices there exists an on-line competitive algorithm for the class of $H$-free bipartite graphs. We then analyze the performance of an on-line algorithm for coloring bipartite graphs on various subfamilies. The algorithm yields new upper bounds for the on-line chromatic number of bipartite graphs. We prove that the algorithm is on-line competitive for $P_7$-free bipartite graphs, i.e., that do not contain an induced path on seven vertices. The number of colors used by the on-line algorithm for $P_6$-free and $P_7$-free bipartite graphs is, respectively, bounded by roughly twice and roughly eight times the on-line chromatic number. In contrast, it is known that there exists no competitive on-line algorithm to color $P_6$-free (or $P_7$-free) bipartite graphs, i.e., for which the number of colors is bounded by any function depending only on the chromatic number.

Additional Information

©2008 Society for Industrial and Applied Mathematics. Received by the editors August 24, 2006; accepted for publication (in revised form) July 17, 2007; published electronically February 8, 2008. An extended abstract of some of the results in this paper was presented at the 6th Italian Conference on Algorithms and Complexity 2006 [3]. We thank the anonymous referees for their useful comments on an earlier version of this paper.

Files

BROsiamjdm08.pdf
Files (271.8 kB)
Name Size Download all
md5:63f0bb0d6042d9d74f4358c976ad7d10
271.8 kB Preview Download

Additional details

Created:
August 22, 2023
Modified:
October 16, 2023