Cohen-Macaulay permutation graphs
arXiv:2310.17343 · doi:10.7146/math.scand.a-149033
Abstract
In this article, we characterize Cohen-Macaulay permutation graphs. In particular, we show that a permutation graph is Cohen-Macaulay if and only if it is well-covered and there exists a unique way of partitioning its vertex set into disjoint maximal cliques, where is the cardinality of a maximal independent set of the graph. We also provide some sufficient conditions for a comparability graph to be a uniquely partially orderable (UPO) graph.
9 pages, 4 figures; comments are welcome