Classification of whist tournaments with up to 12 players

A v-player whist tournament Wh(v) is a schedule of games, each involving two players opposing two others. Every round, the players are partitioned into games, with at most one player left over. Each player partners every other player exactly once and opposes every other player exactly twice during the tournament. Directed whist tournaments DWh(v), and triplewhist tournaments TWh(v), are Wh(v) with certain additional requirements. In this work the nonisomorphic Wh(v), DWh(v), and TWh(v) are enumerated for v6 12. We nd an apparently new Wh(9) and establish that there exists no DWh(12)—and thereby no (12; 4; 1)-RPMD—nor a TWh(12). ? 2003 Elsevier B.V. All rights reserved.