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Hadwiger's Conjecture for Proper Circular Arc Graphs

Naveen Belkale·L. Sunil Chandran
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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 of $k$ vertices is a minor of $G$. We prove Hadwiger's conjecture for proper circular arc graphs.

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BibTeXRIS

Naveen Belkale, L. Sunil Chandran. 2006-07-07. Hadwiger's Conjecture for Proper Circular Arc Graphs. https://arxiv.org/abs/math/0605503

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