Weakening arcs in tournaments

A weakening arc of an irreducible tournament is an arc whose reversal creates a reducible tournament. We consider properties of such arcs and derive recurrence relations for enumerating strong tournaments with no such arcs, one or more such arcs, and exactly one such arc. We also give some asymptotic results on the numbers of such tournaments, among other things. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 142–162, 2004