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 ${\mathsf{M}}_m(C_{2t+1})$ of an odd cycle, Kneser graphs $\mathsf{KG}(n,k)$, and Schrijver graphs $\mathsf{SG}(n,k)$ are not cover graphs when $m⩾0,t⩾1$, $k⩾1$, and $n⩾2k+2$. These results have consequences in circular chromatic number.