Partitioning perfect graphs into comparability graphs
Combinatorics
2026-03-10 v2
Abstract
We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all perfect graphs. On the other hand, we prove that for interval graphs an arbitrarily large number of comparability subgraphs might be necessary.
Keywords
Cite
@article{arxiv.2408.13523,
title = {Partitioning perfect graphs into comparability graphs},
author = {András Gyárfás and Márton Marits and Géza Tóth},
journal= {arXiv preprint arXiv:2408.13523},
year = {2026}
}