Review of: The Ethics of Reproductive Technology (Kenneth D. Alpern ed., Oxford University Press 1992)

Review of: The Ethics of Reproductive Technology (Kenneth D. Alpern ed., Oxford University Press 1992). Additional readings, glossary, introduction, notes, preface. LC 92-8252; ISBN 0-19-507435-1. [370 pp. Paper $19.95. 200 Madison Avenue, New York NY 10016.

Strong games played on random graphs

In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some target structure (such as a clique, a perfect matching, a Hamilton cycle, etc.). It is well known that Red can always ensure at least a draw in any strong game, but finding explicit winning strategies is a difficult and a quite rare task. We consider strong games played on the edge set of a random graph G ~ G(n,p) on n vertices. We prove, for sufficiently large $n$ and a fixed constant 0 < p < 1, that Red can w.h.p win the perfect matching game on a random graph G ~ G(n,p)