Non-h-strong Tournaments and Their Score Vectors

Abstract:

      A tournament T_n of order n is said to be h-strong if every subtournament of order n-h+1 in T_n is strong, and a score vector R_n= (r₁, r₂,… ,r_n) is said to be potentially non-h-strong if there exists some non-h-strong tournament such that its score vector is R_n. The purpose of this paper is to give a crite-rion for determining whether a score vector R_n is potentially non-h-strong.