The tight bound on the number of C_3-free vertices on regular 3-partite tournaments
نویسندگان
چکیده
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 also prove that this bound is tight by giving an infinite family of regular 3-partite tournaments having exactly n 12 −→ C3-free vertices.
منابع مشابه
The 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...
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 52 شماره
صفحات -
تاریخ انتشار 2012