Domination when the stars are out
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Clique minors in claw-free graphs
Journal of Combinatorial Theory Series B
Complete Minors and Independence Number
SIAM Journal on Discrete Mathematics
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Hadwiger's conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class of claw-free graphs (graphs that do not have a vertex with three pairwise nonadjacent neighbors). Our main result is that a claw-free graph with chromatic number χ has a clique minor of size \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}$\lceil\frac{2}{3}\chi\rceil$\end{document}. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 259–278, 2010 Part of this research was conducted while Maria Chudnovsky served as a Clay Mathematics Institute Research Fellow.