ArticleOriginal scientific text
Title
Complete minors, independent sets, and chordal graphs
Authors 1, 2, 1, 1
Affiliations
- Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
- Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA
Abstract
The Hadwiger number h(G) of a graph G is the maximum size of a complete minor of G. Hadwiger's Conjecture states that h(G) ≥ χ(G). Since χ(G) α(G) ≥ |V(G)|, Hadwiger's Conjecture implies that α(G) h(G) ≥ |V(G)|. We show that (2α(G) - ⌈log_{τ}(τα(G)/2)⌉) h(G) ≥ |V(G)| where τ ≍ 6.83. For graphs with α(G) ≥ 14, this improves on a recent result of Kawarabayashi and Song who showed (2α(G) - 2) h(G) ≥ |V(G) | when α(G) ≥ 3.
Keywords
clique minor, independence number, Hadwiger conjecture, chordal graphs
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Pages:
639-674
Main language of publication
English
Received
2009-09-14
Accepted
2010-09-15
Published
2011
DOI: 10.7151/dmgt.1571
Exact and natural sciences