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|Title:||Kings in multipartite tournaments|
|Authors:||Koh, K.M. |
|Source:||Koh, K.M.,Tan, B.P. (1995-12-16). Kings in multipartite tournaments. Discrete Mathematics 147 (1-3) : 171-183. ScholarBank@NUS Repository.|
|Abstract:||Let T be an n-partite tournament and let kr(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) ≥ 1, and found infinitely many bipartite tournaments T with at most one transmitter such that k3 (T) = 0. In this paper, we (i) obtain some sufficient conditions for T to have k3 (T) ≥ 1, (ii) show that if T contains no transmitter, then k4 (T) ≥ 4 when n = 2, and k4 (T) ≥ 3 when n ≥ 3, and (iii) characterize all T with no transmitter such that the equalities in (ii) hold. © 1995.|
|Source Title:||Discrete Mathematics|
|Appears in Collections:||Staff Publications|
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