Let T be an n-partite tournament and let k,(T) denote the number of r-kings of T. Gutin (1986) and Petrovic and Thomassen (1991) proved independently that if T contains at most one transmitter, then k4(T) >i 1, and found infinitely many bipartite tournaments T with at most one transmitter such that
Kings in k-partite tournaments
β Scribed by Vojislav Petrovic; Carsten Thomassen
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 124 KB
- Volume
- 98
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Petrovic, V. and C. Thomassen, Kings in k-partite tournaments, Discrete Mathematics 98 (1991) 237-238.
We prove that every k-partite tournament with at most one vertex of in-degree zero contains a vertex from which each other vertex can be reached in at most four steps.
π SIMILAR VOLUMES
We present a variety of results concerning characterization, number, distribution and some aspects of stability of r-kings (r = 2 4) of bipartite tournaments.
## In [Volkmann, to appear] it is conjectured that all diregular c-partite tournaments, with c β₯ 4, are pancyclic. In this article, we show that all diregular c-partite tournaments, with c β₯ 5, are in fact vertex-pancyclic.
We show that in any bipartite tournament with no transmitters and no 3-kings, the number of 4-kings is at least eight. All such bipartite tournaments having exactly eight 4-kings are completely characterized.
Given a tournament score sequence s 1 s 2 } } } s n , we prove that there exists a tournament T on vertex set [1, 2, ..., n] such that the degree of any vertex i is s i and the subtournaments of T on both the even and the odd vertices are transitive in the given order. This means that i beats j when