On the chromatic number of a subgraph of the Kneser graph

Abstract

Let n and k be positive integers with n≥2k. Consider a circle C with n points 1,…,n in clockwise order. The interlacing graphIGn,k is the graph with vertices corresponding to k-subsets of [n] that do not contain two adjacent points on C, and edges between k-subsets P and Q if they interlace: after removing the points in P from C, the points in Q are in different connected components. In this paper we prove that the circular chromatic number of IGn,k is equal to n/k, hence the chromatic number is ⌈n/k⌉, and that its independence number is (n−k−1k−1).