Boxicity of Circular Arc Graphs

A k-dimensional box is the cartesian product R1 ×R2 × · · · ×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes: that is two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc graph is a graph that can be represented as the intersection graph of arcs on a circle. Let G be a circular arc graph with maximum degree ∆. We show that if ∆ <