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- W2090802004 abstract "Let T be a 3-partite tournament. We say that a vertex v is C 3 ⃗ -free if v does not lie on any directed triangle of T . Let F 3 ( T ) be the set of the C 3 ⃗ -free vertices in a 3-partite tournament and f 3 ( T ) its cardinality. In this paper we prove that if T is a regular 3-partite tournament, then F 3 ( T ) must be contained in one of the partite sets of T . It is also shown that for every regular 3-partite tournament, f 3 ( T ) does not exceed n 9 , where n is the order of T . On the other hand, we give an infinite family of strongly connected tournaments having n − 4 C 3 ⃗ -free vertices. Finally we prove that for every c ≥ 3 there exists an infinite family of strongly connected c -partite tournaments, D c ( T ) , with n − c − 1 C 3 ⃗ -free vertices." @default.
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- W2090802004 date "2010-10-01" @default.
- W2090802004 modified "2023-10-03" @default.
- W2090802004 title "The number of C3⃗-free vertices on 3-partite tournaments" @default.
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- W2090802004 doi "https://doi.org/10.1016/j.disc.2010.06.006" @default.
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