Bollobás-Erdős-Tuza Conjecture for Graphs With No Induced K s , t

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-03-30 DOI:10.1002/jgt.23246

Xinbu Cheng, Zixiang Xu

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引用次数: 0

Abstract

A widely open conjecture proposed by Bollobás, Erdős, and Tuza in the early 1990s states that for any $n$ -vertex graph $G$ , if the independence number $α (G) = Ω (n)$ , then there is a subset $T \subseteq V (G)$ with $∣ T ∣ = o (n)$ such that $T$ intersects all maximum independent sets of $G$ . In this study, we prove that this conjecture holds for graphs that do not contain an induced $K_{s, t}$ for fixed $t \geq s$ . Our proof leverages the probabilistic method at an appropriate juncture.

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Bollobás-Erdős-Tuza无诱导K s， t图的猜想

一个由Bollobás， Erdős和Tuza在20世纪90年代初提出的广泛开放的猜想表明，对于任何n顶点图G，如果独立数α (G) = Ω (n) ,则存在一个子集T≤V (G)，有∣T∣= o (n)满足T与G的所有最大独立集相交。在这项研究中，我们证明了这个猜想对不包含诱导K s的图成立，T表示固定T≥s。我们的证明在适当的时刻利用了概率方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 .