论文标题
在无叉T完美图上
On Fork-free T-perfect Graphs
论文作者
论文摘要
为了理解独立集问题的复杂性，CHV {Á}定义了T-Perfect图。尽管此类的完整表征仍然很大，但对于无爪图[Bruhn and Stein，Math。\ Program。\ program。\ 2012]和$ P_ {5} $ - 免费图[Bruhn and Fuchs，Siam J. \ Inciam J. \ iNcelete Math。\ 2017]。我们又采取了一个步骤来表征无叉的T完美图，并证明它们是强烈的T-完美和三色。我们还提出了用于识别和着色这些图的多项式时间算法。
In an attempt to understanding the complexity of the independent set problem, Chv{á}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.
