When is the Direct Product of Generalized Mycielskians a Cover Graph?

作者：Lai, Hsin-Hao; Lih, Ko-Wei; Lin, Chen-Ying^*; Tong, Li-Da

来源：Ars Combinatoria, 2014, 117: 65-73.

• cover graph
• direct product
• generalized Mycielskian
• circular chromatic number

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. The direct product G x H of graphs G and H is the graph having vertex set V (G) x V (H) and edge set E(G x H) = {(g(i), h(s))(g(i),h(s)) vertical bar g(i)g(j) is an element of E(G) and h(s)h(t) is an element of E(H)}. We prove that the direct product M-m(G) x M-n(H) of the generalized Mycielskians of G and H is a cover graph if and only if G or H is bipartite.

• 出版日期2014-10
• 单位中山大学; 中国科学院