Treewidth of the Kneser graph and the Erdős-Ko-Rado theorem

Abstract

Treewidth is an important and well-known graph parameter that measures the complexity of a graph. The Kneser graph Kneser(n, k) is the graph with vertex set ([n]k), such that two vertices are adjacent if they are disjoint. We determine, for large values of n with respect to k, the exact treewidth of the Kneser graph. In the process of doing so, we also prove a strengthening of the Erdo{double acute}s-Ko-Rado Theorem (for large n with respect to k) when a number of disjoint pairs of k-sets are allowed.