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 $\left(\genfrac{}{}{0ex}{}{[n]}{k}\right)$, 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 Erdős-Ko-Rado Theorem (for large n with respect to k) when a number of disjoint pairs of k-sets are allowed.

arXiv comment10 pages, 0 figures