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Suppose D is an acyclic orientation of a graph G. An arc of D is said to be independent if its reversal results in another acyclic orientation. Let i(D) denote the number of independent arcs in D, and let N(G)={i(D):D is an acyclic orientation of G}. Also, let imin(G) be the minimum of N(G) and imax(G) the maximum. While it is known that imin(G)=|V(G)|−1 for any connected graph G, the present paper...
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 Mm(C2t+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⩾2k+2. These results have consequences in circular chromatic number.
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