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Almost-spanning Universality in Random Graphs by Conlon, David; Ferber, Asaf; Nenadov, Rajko; Škorić, Nemanja is a scholarly article available to read on EtoBox.

What is Almost-spanning Universality in Random Graphs about?

A graph $G$ is said to be $\mathcal H(n,\Delta)$-universal if it contains every graph on $n$ vertices with maximum degree at most $\Delta$. It is known that for any $\varepsilon > 0$ and any natural number $\Delta$ there exists $c > 0$ such that the random graph $G(n,p)$ is asymptotically almost surely $\mathcal H((1-\varepsilon)n,\Delta)$-universal for $p \geq c (\log n/n)^{1/\Delta}$. Bypassing this natural boundary, we show that for $\Delta \geq 3$ the same conclusion holds when $p = \omega\left(n^{-\frac{1}{\Delta-1}}\log^5 n\right)$.

Author

Conlon, David; Ferber, Asaf; Nenadov, Rajko; Škorić, Nemanja

Published

2015

Language

EN