Competition periods of multipartite tournaments

Abstract

© 2022 Informa UK Limited, trading as Taylor & Francis Group.The adjacency matrix of a k-partite tournament for (Formula presented.) is represented as a (Formula presented.) Boolean block matrix A with blocks (Formula presented.) for (Formula presented.) such that (Formula presented.) is a zero matrix; (Formula presented.) is a matrix with all elements equal to 1 for (Formula presented.) where (Formula presented.) means the transpose of (Formula presented.). There is the smallest positive integer q such that (Formula presented.) for some positive integer r and every nonnegative integer i. Then there is also the smallest positive integer p such that (Formula presented.). In this paper, we show that (Formula presented.), and, further, if k = 2, then (Formula presented.).