Hadwiger's conjecture for quasi-line graphs

Maria Chudnovsky; Alexandra Ovetsky Fradkin

doi:10.1002/jgt.20321

Hadwiger's conjecture for quasi-line graphs

Maria Chudnovsky, Alexandra Ovetsky Fradkin

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

A graph G is a quasi-line graph if for every vertex v ∈ V(G), the set of neighbors of v in G can be expressed as the union of two cliques. The class of quasi-line graphs is a proper superset of the class of line graphs. Hadwiger's conjecture states that if a graph G is not t-colorable then it contains K_t+1 as a minor. This conjecture has been proved for line graphs by Reed and Seymour. We extend their result to all quasi-line graphs.

Original language	English (US)
Pages (from-to)	17-33
Number of pages	17
Journal	Journal of Graph Theory
Volume	59
Issue number	1
DOIs	https://doi.org/10.1002/jgt.20321
State	Published - Sep 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Claw-free graphs
Hadwiger's conjecture
Minors

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10.1002/jgt.20321

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Hadwiger's conjecture for quasi-line graphs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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