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Spanning trees in graphs without large bipartite holes

Published online by Cambridge University Press:  14 November 2023

Jie Han
School of Mathematics and Statistics and Center for Applied Mathematics, Beijing Institute of Technology, Beijing, China
Jie Hu
Center for Combinatorics and LPMC, Nankai University, Tianjin, China
Lidan Ping
School of Mathematics, Shandong University, Jinan, China
Guanghui Wang
School of Mathematics, Shandong University, Jinan, China
Yi Wang
Data Science Institute, Shandong University, Jinan, China
Donglei Yang*
School of Mathematics, Shandong University, Jinan, China
Corresponding author: Donglei Yang; Email:


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.

MSC classification

Secondary: 05C05: Trees
© The Author(s), 2023. Published by Cambridge University Press

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Jie Hu: Supported by Natural Science Foundation of China (12131013, 12161141006). Guanghui Wang: Research supported by Natural Science Foundation of China (12231018) and Young Taishan Scholars probgram of Shandong Province (201909001). Donglei Yang: Supported by the China Post-doctoral Science Foundation (2021T140413), Natural Science Foundation of China (12101365) and Natural ScienceFoundation of Shandong Province (ZR2021QA029).


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