When is the Direct Product of Generalized Mycielskians a Cover Graph?
Combinatorics
2012-02-28 v1
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. 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_j,h_t): g_ig_j belongs to E(G) and h_sh_t belongs to 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.
Keywords
Cite
@article{arxiv.1202.5720,
title = {When is the Direct Product of Generalized Mycielskians a Cover Graph?},
author = {Hsin-Hao Lai and Ko-Wei Lih and Chen-Ying Lin and Li-Da Tong},
journal= {arXiv preprint arXiv:1202.5720},
year = {2012}
}
Comments
9 pages, accepted by Ars Combinatoria on May 13, 2010