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Cliques, minors and apex graphs

✍ Scribed by Jianbing Niu; Cun-Quan Zhang

Book ID
108114112
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
820 KB
Volume
309
Category
Article
ISSN
0012-365X

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## Abstract The Hadwiger number ${h}({G})$ of a graph __G__ is the maximum integer __t__ such that ${K}\_{t}$ is a minor of __G__. Since $\chi({G})\cdot\alpha({G})\geq |{G}|$, Hadwiger's conjecture implies that ${h}({G})\cdot \alpha({G})\geq |{G}|$, where $\alpha({G})$ and $|{G}|$ denote the indepe