Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, November 23, 2006, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Reto Spöhel

Asymmetric Ramsey Properties of Random Graphs

Consider the following problem: Find a coloring of the edges of the random graph $G_{n,p}$ with $k$ colors such that there is no monochromatic copy of some fixed graph $F$. Rödl and Rucinski (1995) proved a general threshold function $p_0(F,n)$ for the existence of such a coloring Their proof was, however, non-constructive.

Kohayakawa and Kreuter (1997) conjectured a general threshold formula for the asymmetric case, where a different graph $F_i$ is forbidden in every color $i$, $1\leq i\leq k$. They verified it for the case when all graphs involved are cycles, but all other cases have remained open.

We address the case when all graphs involved are cliques and propose an algorithm that a.a.s. finds a valid $k$-edge-coloring of $\Gnp$ when $p$ is below the conjectured threshold. This algorithm can be also adjusted to produce a valid $k$-coloring in the symmetric case.

Joint work with Martin Marciniszyn, Jozef Skokan, and Angelika Steger.

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