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Embedding bounded degree spanning trees in random graphs

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arxiv 1405.6559 v2 pith:DWNWMMF2 submitted 2014-05-26 math.CO

Richard Montgomery This is my paper
classification math.CO
keywords degreedeltarandomalmostboundedcopyembeddingfound
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abstract

We prove that if a tree $T$ has $n$ vertices and maximum degree at most $\Delta$, then a copy of $T$ can almost surely be found in the random graph $\mathcal{G}(n,\Delta\log^5 n/n)$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Universality in random graphs via optimal linking systems: trees and beyond

    math.CO 2026-08 conditional novelty 8.0 of 10

    An absolute constant C suffices for bounded-degree tree universality in G(n, C ln n/n), and cycle-factor universality is optimal up to constants via depth-optimal linking systems.

  2. Spanning trees of bounded degree in random geometric graphs

    math.CO 2025-05 conditional novelty 7.0 of 10

    Random geometric graphs have a sharp threshold, radius sqrt(d log(Δ-1)/(2 log n)), for containing every n-vertex tree of maximum degree at most Δ.

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