Spanning trees in graphs without large bipartite holes

IF 0.9 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Combinatorics, Probability & Computing Pub Date : 2023-11-14 DOI:10.1017/s0963548323000378

Jie Han, Jie Hu, Lidan Ping, Guanghui Wang, Yi Wang, Donglei Yang

引用次数: 0

Abstract

Abstract We show that for any $\varepsilon \gt 0$ and $\Delta \in \mathbb{N}$ , there exists $\alpha \gt 0$ such that for sufficiently large $n$ , every $n$ -vertex graph $G$ satisfying that $\delta (G)\geq \varepsilon n$ and $e(X, Y)\gt 0$ for every pair of disjoint vertex sets $X, Y\subseteq V(G)$ of size $\alpha n$ contains all spanning trees with maximum degree at most $\Delta$ . This strengthens a result of Böttcher, Han, Kohayakawa, Montgomery, Parczyk, and Person.

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无大二部孔图中的生成树

摘要我们证明了对于任意$\varepsilon \gt 0$和$\Delta \in \mathbb{N}$，存在这样的$\alpha \gt 0$，对于足够大的$n$，每一个$n$ -顶点图$G$满足$\delta (G)\geq \varepsilon n$和$e(X, Y)\gt 0$对于每一对大小为$\alpha n$的不相交顶点集$X, Y\subseteq V(G)$包含所有最大度的生成树$\Delta$。这加强了Böttcher、Han、Kohayakawa、Montgomery、Parczyk和Person的研究结果。

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

Combinatorics, Probability & Computing 数学-计算机：理论方法

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.