Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, November 27, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Reto Spöhel

Small subgraphs in random graphs and the power of multiple choices: The offline case

Consider the following problem: We are given a graph $G_{n,m}$ drawn uniformly at random from all graphs on $n$ vertices with $m$ edges, and a random partition of its edge set into sets of size $r$ called $r$-sets. Here $r\geq 2$ is a fixed integer, and we assume w.l.o.g. that $m$ is divisible by $r$. We want to select one edge from each $r$-set such that the resulting subgraph of $G_{n,m}$ does not contain a copy of some fixed forbidden graph $F$. How large can $m=m(n)$ be such that this is still possible with probability $1-o(1)$?

We prove an explicit threshold function $m_0(F,r,n)$ for this problem, valid for any graph $F$ and any integer $r\geq 2$.

Joint work with Michael Krivelevich and Angelika Steger.

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