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1 results

Spanning trees in graphs without large bipartite holes
Part of
- Graph theory
Jie Han, Jie Hu, Lidan Ping, Guanghui Wang, Yi Wang, Donglei Yang
Journal:

Combinatorics, Probability and Computing / Volume 33 / Issue 3 / May 2024

Published online by Cambridge University Press:

14 November 2023, pp. 270-285
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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.