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Spanning trees in the square of pseudorandom graphs

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arxiv 2307.00322 v2 pith:GWARXM6C submitted 2023-07-01 math.CO

Matías Pavez-Signé This is my paper · ORCID
classification math.CO
keywords deltaeverylambdaanswersboundedconstantcontainsdegree
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abstract

We show that for every $\Delta\in\mathbb N$, there exists a constant $C$ such that if $G$ is an $(n,d,\lambda)$-graph with $d/\lambda\ge C$ and $d$ is large enough, then $G^2$ contains every $n$-vertex tree with maximum degree bounded by $\Delta$. This answers a question of Krivelevich.

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Cited by 1 Pith paper

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  1. Tree tilings in random regular graphs

    math.CO 2024-12 accept novelty 8.0 of 10

    For every fixed epsilon, with high probability the random d-regular graph contains a vertex-partition into copies of any prescribed tree of size at most (1-epsilon)d/ln d.

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