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arXiv · 2211.03538

On Fork-free T-perfect Graphs

Yixin Cao·Shenghua Wang
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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 $P_{5}$-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.

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Yixin Cao, Shenghua Wang. 2022-11-07. On Fork-free T-perfect Graphs. https://arxiv.org/abs/2211.03538

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