Hadwiger's Conjecture for the Complements of Kneser Graphs

Hadwiger's conjecture asserts that every graph with chromatic number t contains a complete minor of order t . Given integers n ≥ 2 k + 1 ≥ 5 , the Kneser graph K ( n , k ) is the graph with vertices the k ‐subsets of an n ‐set such that two vertices are adjacent if and only if the corresponding k ‐subsets are disjoint. We prove that Hadwiger's conjecture is true for the complements of Kneser graphs.