Hadwiger’s conjecture for proper circular arc graphs

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.