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#### On the probability of rendezvous in graphs

##### MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44318

Dietzfelbinger,  Martin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45588

Tamaki,  Hisao
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

##### Locator
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##### Fulltext (public)

2003-1-006
(Any fulltext), 10KB

##### Supplementary Material (public)
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##### Citation

Dietzfelbinger, M., & Tamaki, H.(2003). On the probability of rendezvous in graphs (MPI-I-2003-1-006). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-6B83-7
##### Abstract
In a simple graph $G$ without isolated nodes the following random experiment is carried out: each node chooses one of its neighbors uniformly at random. We say a rendezvous occurs if there are adjacent nodes $u$ and $v$ such that $u$ chooses $v$ and $v$ chooses $u$; the probability that this happens is denoted by $s(G)$. M{\'e}tivier \emph{et al.} (2000) asked whether it is true that $s(G)\ge s(K_n)$ for all $n$-node graphs $G$, where $K_n$ is the complete graph on $n$ nodes. We show that this is the case. Moreover, we show that evaluating $s(G)$ for a given graph $G$ is a \numberP-complete problem, even if only $d$-regular graphs are considered, for any $d\ge5$.