On-line coloring of h-free bipartite graphs

Authors:
H. J. Broersma;A. Capponi;D. Paulusma
Affiliations:
Department of Computer Science, Durham University, Durham, England;Computer Science, Division of Engineering and Applied Sciences, California Institute of Technology;Department of Computer Science, Durham University, Durham, England
Venue:
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Year:
2006

Citing 10
Cited 1

The linearity of first-fit coloring of interval graphs

SIAM Journal on Discrete Mathematics
An on-line graph coloring algorithm with sublinear performance ratio

Discrete Mathematics
On-Line Coloring and Recursive Graph Theory

SIAM Journal on Discrete Mathematics
Radius two trees specify &khgr;-bounded classes

Journal of Graph Theory
On the on-line chromatic number of the family of on-line 3-chromatic graphs

Discrete Mathematics - Special issue: selected papers in honour of Paul Erdo&huml;s on the occasion of his 80th birthday
On-line 3-chromatic graphs—II: critical graphs

Discrete Mathematics
On-line coloring of geometric intersection graphs

Computational Geometry: Theory and Applications
Coloring Graphs On-line

Developments from a June 1996 seminar on Online algorithms: the state of the art
Vertex Colouring and Forbidden Subgraphs – A Survey

Graphs and Combinatorics
Graph Theory With Applications

Graph Theory With Applications

Online hypergraph coloring

Information Processing Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a new on-line algorithm for coloring bipartite graphs. This yields a new upper bound on the on-line chromatic number of bipartite graphs, improving a bound due to Lovász, Saks and Trotter. The algorithm is on-line competitive on various classes of H – free bipartite graphs, in particular P6-free bipartite graphs and P7-free bipartite graphs, i.e., that do not contain an induced path on six, respectively seven vertices. The number of colors used by the on-line algorithm in these particular cases is bounded by roughly twice, respectively roughly eight times the on-line chromatic number. In contrast, it is known that there exists no competitive on-line algorithm to color P6-free (or P7-free) bipartite graphs, i.e., for which the number of colors is bounded by any function only depending on the chromatic number.