A Constructive Solution to a Tournament Problem
- 1 January 1971
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 14 (1) , 45-48
- https://doi.org/10.4153/cmb-1971-007-1
Abstract
By a tournament Tn on n vertices, we shall mean a directed graph on n vertices for which every pair of distinct vertices form the endpoints of exactly one directed edge (e.g., see [5]). If x and y are vertices of Tn we say that x dominates y if the edge between x and y is directed from x to y. In 1962, K. Schütte [2] raised the following question: Given k > 0, is there a tournament Tn(k) such that for any set S of k vertices of Tn(k) there is a vertex y which dominates all k elements of S. (Such a tournament will be said to have property Pk.)Keywords
This publication has 3 references indexed in Scilit:
- On a Problem of Schütte and ErdösThe Mathematical Gazette, 1965
- On a Problem in Graph TheoryThe Mathematical Gazette, 1963
- On Character Sums and Primitive Roots†Proceedings of the London Mathematical Society, 1962