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arXiv · 1802.04707

Universality for bounded degree spanning trees in randomly perturbed graphs

Julia Böttcher·Jie Han·Yoshiharu Kohayakawa·Richard Montgomery·Olaf Parczyk·Yury Person
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Abstract

We solve a problem of Krivelevich, Kwan and Sudakov [SIAM Journal on Discrete Mathematics 31 (2017), 155-171] concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs. More precisely, we show that, if we start with a dense graph $G_\alpha$ on $n$ vertices with $\delta(G_\alpha)\ge \alpha n$ for $\alpha>0$ and we add to it the binomial random graph $G(n,C/n)$, then with high probability the graph $G_\alpha\cup G(n,C/n)$ contains copies of all spanning trees with maximum degree at most $\Delta$ simultaneously, where $C$ depends only on $\alpha$ and $\Delta$.

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Julia Böttcher, Jie Han, Yoshiharu Kohayakawa, Richard Montgomery, Olaf Parczyk, Yury Person. 2018-02-13. Universality for bounded degree spanning trees in randomly perturbed graphs. https://arxiv.org/abs/1802.04707

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