## 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: Tuesday, February 03, 2009, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Sonny Ben-Shimon (Tel Aviv Univ.)

## Local resilience of regular graphs

Given an increasing monotone graph property $\mathcal{P}$, the local resilience of a graph $G$ with respect to $\mathcal{P}$ is the minimum $r$ for which $G$ contains a subgraph $H$ of maximal degree $\Delta(H)=r$ such that $G-H$ does not posses $\mathcal{P}$. Although this notion had been previously studied implicitly for some graph properties and graph families, it was only recently that a systematic approach to the problem was initiated by Sudakov and Vu. The main focus of the original work of Sudakov and Vu and of subsequent works was in the resilience of random and pseudorandom graphs with respect to several graph properties. In this talk we continue to explore this notion of local resilience of graphs, where our graphs are random and pseudorandom regular graphs. Specifically, we explore the local resilience of regular graphs with respect to edge-connectivity, containing a perfect matching, and being Hamiltonian.

Joint work in progress with M. Krivelevich and B. Sudakov.

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