No 17‐player triplewhist tournament has nontrivial automorphisms

Abstract The existence of triplewhist tournaments for v players has recently been solved for all values of v except = 17. For v = 12 and v = 13, a complete enumeration has shown the nonexistence of TWh(v), while constructions of TWh(v) have been presented for v > 17. For several values of v, existence has been shown by constructing a TWh(v) with a prescribed, usually cyclic, automorphism group. In this article, it is shown that the strategy of constructing a TWh(v) with a prescribed automorphism group cannot succeed with TWh(17), since no 17‐player triplewhist tournament has nontrivial automorphisms. © 2004 Wiley Periodicals, Inc.