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Spanning trees in graphs without large bipartite holes
Published online by Cambridge University Press: 14 November 2023
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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- © The Author(s), 2023. Published by Cambridge University Press
Footnotes
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).