## 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, September 16, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Stefanie Gerke (Royal Holloway, Univ. of London)

## Uniform Random Intersection Graph

A \emph{uniform random intersection graph} $G(n,m,k)$ is a random graph constructed as follows. Label each of $n$ nodes by a randomly chosen set of $k$ distinct colours taken from some finite set of possible colours of size $m$. Nodes are joined by an edge if and only if some colour appears in both their labels. These graphs arise in the study of the security of wireless sensor networks. Such graphs arise in particular when modelling the network graph of the well known key predistribution technique due to Eschenauer and Gligor.

In this talk we consider the threshold for connectivity and the appearance of a giant component of the graph $G(n,m,k)$ when $n\rightarrow \infty$ with $k$ a function of $n$ such that $k\geq 2$ and $m=\lfloor n^\alpha\rfloor$ for some fixed positive real number $\alpha$.

Information for students and suggested topics for student talks