Non-cover generalized Mycielski, Kneser, and Schrijver graphs

Abstract

A graph is said to be a cover graph if it is the underlying graph of the Hasse diagram of a finite partially ordered set. We prove that the generalized Mycielski graphs M m ( C 2 t + 1 ) of an odd cycle, Kneser graphs KG ( n , k ) , and Schrijver graphs SG ( n , k ) are not cover graphs when m ⩾ 0 , t ⩾ 1 , k ⩾ 1 , and n ⩾ 2 k + 2 . These results have consequences in circular chromatic number.