English

On Fork-free T-perfect Graphs

Discrete Mathematics 2022-11-08 v1 Combinatorics

Abstract

In an attempt to understanding the complexity of the independent set problem, Chv{\'a}tal defined t-perfect graphs. While a full characterization of this class is still at large, progress has been achieved for claw-free graphs [Bruhn and Stein, Math.\ Program.\ 2012] and P5P_{5}-free graphs [Bruhn and Fuchs, SIAM J.\ Discrete Math.\ 2017]. We take one more step to characterize fork-free t-perfect graphs, and show that they are strongly t-perfect and three-colorable. We also present polynomial-time algorithms for recognizing and coloring these graphs.

Keywords

Cite

@article{arxiv.2211.03538,
  title  = {On Fork-free T-perfect Graphs},
  author = {Yixin Cao and Shenghua Wang},
  journal= {arXiv preprint arXiv:2211.03538},
  year   = {2022}
}
R2 v1 2026-06-28T05:19:31.067Z