Hadwiger's conjecture for proper circular arc graphs

Authors:
Naveen Belkale;L. Sunil Chandran
Affiliations:
CSA Department, IISc, Bangalore, Pin-560012, India;CSA Department, IISc, Bangalore, Pin-560012, India
Venue:
European Journal of Combinatorics
Year:
2009

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Abstract

Circular arc graphs are graphs whose vertices can be represented as arcs on a circle such that any two vertices are adjacent if and only if their corresponding arcs intersect. Proper circular arc graphs are graphs which have a circular arc representation where no arc is completely contained in any other arc. Hadwiger's conjecture states that if a graph G has chromatic number k, then a complete graph with k vertices is a minor of G. We prove Hadwiger's conjecture for proper circular arc graphs.