Universality for bounded degree spanning trees in randomly perturbed graphs |
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Authors: | Julia Bttcher Jie Han Yoshiharu Kohayakawa Richard Montgomery Olaf Parczyk Yury Person |
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Institution: | 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 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 Gα on n vertices with δ(Gα) ≥ αn for α > 0 and we add to it the binomial random graph G(n,C/n), then with high probability the graph Gα∪G(n,C/n) contains copies of all spanning trees with maximum degree at most Δ simultaneously, where C depends only on α and Δ. |
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Keywords: | perturbed graphs random graphs spanning trees universality |
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