In 1978, K. B. Reid proposed a conjecture as follows: 'Every finite and nonempty set S of positive integers is a set of scores for some tournaments'. And he proved that the conjecture is true for |S|=1, 2, 3. In 1984,...
In 1978, K. B. Reid proposed a conjecture, i.e. 'every finite and nonempty set S of positive integers is a set of scores for some tournaments.' And he proved that the conjecture is true for |S|= 1, 2, 3. In 1984, M. H...
An n-tournament T_n is called k-reducible if auy of its (n--k+1)-subtourna-ments is reducible. An n-tournament T_n is called exactly k-reducible if it is k-reducible but not (k+1)-reducible. The numbers of all isomorp...
Let Tn denote an n-tournament. According to L. Lovász, Tn is called k-P if any of its subtournaments induced by n + 1-κ vertices in Tn has the property P, where P denotes an invariant property of tournaments, either...
A. tournament T = (V, A) is said to be arc-h-cyclic. If for every are e∈A, there is a circuit of length h containing e. When |Ⅴ| =p, an arc-pcyclic tournament is also said to be are-Hamiltonian. Shao Pingzhong and Z...