Universality for bounded degree spanning trees in randomly perturbed graphs
Böttcher, J.
, Han, J., Kohayakawa, Y., Montgomery, R., Parczyk, O. & Person, Y.
(2019).
Universality for bounded degree spanning trees in randomly perturbed graphs.
Random Structures and Algorithms,
55(4), 854-864.
https://doi.org/10.1002/rsa.20850
, Han, J., Kohayakawa, Y., Montgomery, R., Parczyk, O. & Person, Y.
(2019).
Universality for bounded degree spanning trees in randomly perturbed graphs.
Random Structures and Algorithms,
55(4), 854-864.
https://doi.org/10.1002/rsa.20850
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 G α on n vertices with δ(G α ) ≥ αn for α > 0 and we add to it the binomial random graph G(n,C/n), then with high probability the graph G α ∪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.
