ArticleOriginal scientific text

Title

On-line -coloring of graphs

Authors 1

Affiliations

  1. Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland

Abstract

For a given induced hereditary property , a -coloring of a graph G is an assignment of one color to each vertex such that the subgraphs induced by each of the color classes have property . We consider the effectiveness of on-line -coloring algorithms and give the generalizations and extensions of selected results known for on-line proper coloring algorithms. We prove a linear lower bound for the performance guarantee function of any stingy on-line -coloring algorithm. In the class of generalized trees, we characterize graphs critical for the greedy -coloring. A class of graphs for which a greedy algorithm always generates optimal -colorings for the property = K₃-free is given.

Keywords

on-line algorithm, graph coloring, hereditary property

Bibliography

  1. D.R. Bean, Effective coloration, J. Symbolic Logic 41 (1976) 469-480, doi: 10.2307/2272247.
  2. M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
  3. P. Borowiecki, On-line coloring of graphs, in: M. Kubale ed., Graph Colorings, Contemporary Mathematics 352 (American Mathematical Society, 2004) 21-33.
  4. A. Gyárfás and J. Lehel, First-Fit and on-line chromatic number of families of graphs, Ars Combinatoria 29C (1990) 168-176.
  5. H.A. Kierstead, Coloring Graphs On-line, in: A. Fiat and G.J. Woeginger eds., Online Algorithms - The State of the Art, LNCS 1442 (Springer, Berlin, 1998) 281-305.
Pages:
389-401
Main language of publication
English
Received
2006-01-12
Accepted
2006-10-24
Published
2006
Exact and natural sciences