Hadwiger's conjecture for quasi‐line graphs | Zendy

Chudnovsky Maria | Zendy; Fradkin Alexandra Ovetsky | Zendy

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Hadwiger's conjecture for quasi‐line graphs

Author(s) -

Chudnovsky Maria,

Fradkin Alexandra Ovetsky

Publication year - 2008

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.20321

Subject(s) - combinatorics , mathematics , discrete mathematics , conjecture , line graph , pathwidth , chordal graph , block graph , graph

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. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 17–33, 2008

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