关于无叉t-完美图

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2026-10-12 Epub Date: 2026-06-13 DOI:10.1002/jgt.70085

Yixin Cao, Shenghua Wang

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引用次数: 0

摘要

为了理解最大独立集问题的复杂性，Chvátal引入了t-完美图。虽然该类的完整表征仍然开放，但在无爪图方面已经取得了重要进展[Bruhn and Stein， Math]。p5自由图[Bruhn and Fuchs， SIAM J. Discrete mathematics . 2017]。我们进一步刻画了无叉t-完美图，并证明了它们是强t-完美的和可三色的。我们也给出了识别和上色无分叉t-完美图的多项式时间算法。

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On Fork-Free t-Perfect Graphs

In an effort to understand the complexity of the maximum independent set problem, Chvátal introduced t-perfect graphs. While a full characterization of this class remains open, important progress has been made 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 a further step by characterizing fork-free t-perfect graphs and showing that they are strongly t-perfect and 3-colorable. We also give polynomial-time algorithms for recognizing and coloring fork-free t-perfect graphs.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .