Cohen-Macaulay permutation graphs
Commutative Algebra
2024-11-07 v2 Combinatorics
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.
Cite
@article{arxiv.2310.17343,
title = {Cohen-Macaulay permutation graphs},
author = {P. V. Cheri and Deblina Dey and Akhil K and Nirmal Kotal and Dharm Veer},
journal= {arXiv preprint arXiv:2310.17343},
year = {2024}
}
Comments
9 pages, 4 figures; comments are welcome