منابع مشابه
On the 3-kings and 4-kings in multipartite tournaments
Koh and Tan gave a sufficient condition for a 3-partite tournament to have at least one 3-king in [K.M. Koh, B.P. Tan, Kings in multipartite tournaments, Discrete Math. 147 (1995) 171–183, Theorem 2]. In Theorem 1 of this paper, we extend this result to n-partite tournaments, where n 3. In [K.M. Koh, B.P. Tan, Number of 4-kings in bipartite tournaments with no 3-kings, Discrete Math. 154 (1996)...
متن کاملThe number of C3-free vertices on 3-partite tournaments
Let T be a 3-partite tournament. We say that a vertex v is −→ C3 -free if v does not lie on any directed triangle of T . Let F3(T ) be the set of the −→ C3 -free vertices in a 3-partite tournament and f3(T ) its cardinality. In this paper we prove that if T is a regular 3-partite tournament, then F3(T )must be contained in one of the partite sets of T . It is also shown that for every regular 3...
متن کاملNotes on cycles through a vertex or an arc in regular 3-partite tournaments
We shall assume that the reader is familiar with standard terminology on directed graphs (see, e.g., Bang-Jensen and Gutin [1]). In this note, if we speak of a cycle, then we mean a directed cycle. If xy is an arc of a digraph D, then we write x → y and say x dominates y. If X and Y are two disjoint vertex sets of a digraph D such that every vertex of X dominates every vertex of Y , then we say...
متن کاملThe tight bound on the number of C_3-free vertices on regular 3-partite tournaments
Let T be a 3-partite tournament. We say that a vertex v is −→ C3-free if v does not lie on any directed triangle of T . Let F3(T ) be the set of the −→ C3-free vertices in a 3-partite tournament and f3(T ) its cardinality. In a recent paper, it was proved that if T is a regular 3-partite tournament, then f3(T ) < n 9 , where n is the order of T . In this paper, we prove that f3(T ) ≤ n 12 . We ...
متن کاملMedians of Graphs and Kings of Tournaments*
We first prove that for any graph G with a positive vertex weight function w, there exists a graph H with a positive weight function w′ such that w(v) = w′(v) for all vertices v in G and whose w′-median is G. This is a generalization of a previous result for the case in which all weights are 1. The second result is that for any n-tournament T without transmitters, there exists an integer m ≤ 2n...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.11.095