Complementation in t-perfect graphs
Abstract
Inspired by applications of perfect graphs in combinatorial optimization, Chv\'{a}tal defined t-perfect graphs in 1970s. The long efforts of characterizing t-perfect graphs started immediately, but embarrassingly, even a working conjecture on it is still missing after nearly 50 years. Unlike perfect graphs, t-perfect graphs are not closed under substitution or complementation. A full characterization of t-perfection with respect to substitution has been obtained by Benchetrit in his Ph.D. thesis. Through the present work we attempt to understand t-perfection with respect to complementation. In particular, we show that there are only five pairs of graphs such that both the graphs and their complements are minimally t-imperfect.
Cite
@article{arxiv.2104.14935,
title = {Complementation in t-perfect graphs},
author = {Yixin Cao and Shenghua Wang},
journal= {arXiv preprint arXiv:2104.14935},
year = {2021}
}
Comments
Accepted to WG 2021