Reconstruction of complete interval tournaments

Let a, b and n be nonnegative integers (b a, b > 0, n 1), Gn(a, b) be a multigraph on n vertices in which any pair of vertices is connected with at least a and at most b edges and v = (v1, v2, . . . , vn) be a vector containing n nonnegative integers. We give a necessary and sufficient condition for the existence of such orientation of the edges of Gn(a, b), that the resulted out-degree vector equals to v. We describe a reconstruction algorithm. In worst case checking of v requires (n) time and the reconstruction algorithm works in O(bn3 ) time. Theorems of H. G. Landau (1953) and J. W. Moon (1963) on the score sequences of tournaments are special cases b = a = 1 resp. b = a 1 of our result.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Antal Iványi
• Keywords: CORR 2010, Education, Nonnegative Integers, Reconstruction Algorithm, Sufficient Condition