Almost-spanning universality in random graphs (Extended abstract)
asaf ferber2015, Electronic Notes in Discrete Mathematics
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Abstract
A graph G is said to be H(n, ∆)-universal if it contains every graph on at most n vertices with maximum degree at most ∆. It is known that for any ε > 0 and any natural number ∆ there exists c > 0 such that the random graph G(n, p) is asymptotically almost surely H((1 − ε)n, ∆)universal for p ≥ c(log n/n) 1/∆. Bypassing this natural boundary, we show that for ∆ ≥ 3 the same conclusion holds when p ≫ n − 1 ∆−1 log 5 n.
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