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.

翻译：为了了解独立设置问题的复杂性,Chv_'a}tal定义了t-perfect 图形。虽然对这一类图的全面定性仍然很广,但无爪图[Bruhn and Stein, Math.\ program.\ 2012] 和$P%5}$free 图[Bruhn and Fuchs, SIAM J.\ discrete Math.\ 2017] 已经取得了进展。我们又迈出了一步来给无叉 t-perfect 图形定性,并表明它们非常特优和3色。我们还提出了识别和显示这些图表的多时算法。