Treewidth of the Kneser Graph and the Erdős-Ko-Rado Theorem

Daniel J. Harvey, David R. Wood

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

Keywords


graph theory; Kneser graph; treewidth; separators; Erdős-Ko-Rado

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