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 on k vertices is a minor of G. We prove Hadwiger's conjecture for proper circular arc graphs.Definition 4 Complete graph of order n is a graph on n vertices where all the vertices are pairwise adjacent and is denoted by K n .See Diestel [2] for more information on minors.In 1943, Hadwiger made the famous conjecture linking the chromatic number of a graph with its clique minor:Conjecture 5 (Hadwiger [9]) If a graph G has chromatic number χ(G) = r, then K r is a minor of G.

No abstract