# Calendar

Discrete Math

## "Embedding Large Graphs in Random Graphs"

Location:
Date & time: Monday, 03 April 2017 at 2:00PM - 3:00PM

### "Embedding Large Graphs in Random Graphs"

Time: 2:00 PM
Location: Hill 705
Abstract: In this talk, we consider the problem of embedding almost-spanning, bounded degree graphs in a random graph. In particular, let $$Deltageq 5$$, $$varepsilon > 0$$ and let $$H$$ be a graph on $$(1-varepsilon)n$$ vertices and with maximum degree $$Delta$$. We show that a random graph $$G_{n,p}$$ with high probability contains a copy of $$H$$, provided that $$pgg (n^{-1}log^{1/Delta}n)^{2/(Delta+1)}$$. Our assumption on $$p$$ is optimal up to the $$polylog$$ factor. Time permitting, we will discuss recent progress on the "universality" problem, which entails finding the threshold for all graphs of degree at most $$Delta$$ to appear in $$G_{n,p}$$ emph{simultaneously}.

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