First-fit coloring on interval graphs has performance ratio at least 5
Combinatorics
2015-06-02 v1
Abstract
First-fit is the online graph coloring algorithm that considers vertices one at a time in some order and assigns each vertex the least positive integer not used already on a neighbor. The maximum number of colors used by first-fit on graph G over all vertex orders is denoted \chi_{FF}(G). The exact value of R := \sup_G [\chi_{FF}(G) / \omega(G)] over interval graphs G is unknown. Pemmaraju, Raman, and Varadarajan (2004) proved R <= 10, and this can be improved to 8. Witsenhausen (1976) and Chrobak and \'Slusarek (1988) showed R >= 4, and \'Slusarek (1993) improved this to 4.45. We prove R >= 5.
Keywords
Cite
@article{arxiv.1506.00192,
title = {First-fit coloring on interval graphs has performance ratio at least 5},
author = {H. A. Kierstead and David A. Smith and W. T. Trotter},
journal= {arXiv preprint arXiv:1506.00192},
year = {2015}
}
Comments
Accepted to the European Journal of Combinatorics