Hadwiger's Conjecture for Proper Circular Arc Graphs

Details Hadwiger's Conjecture for Proper Circular Arc Graphs Hadwiger's Conjecture for Proper Circular Arc Graphs

2006-05-18

arxiv.org/abs/math/0605503v2

Mathematics

Combinatorics

18 pages, 2 figures

Scientific paper

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 of $k$ vertices is a minor of $G$. We prove Hadwiger's conjecture for proper circular arc graphs.

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