@techreport{MPI-I-94-224,
TITLE = {On the probability of rendezvous in graphs},
AUTHOR = {Dietzfelbinger, Martin and Tamaki, Hisao},
LANGUAGE = {eng},
NUMBER = {MPI-I-2003-1-006},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {2003},
DATE = {2003},
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 $d\ge5$.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}