Please use this identifier to cite or link to this item:
https://doi.org/10.1016/j.disc.2006.04.023
DC Field | Value | |
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dc.title | On the 3-kings and 4-kings in multipartite tournaments | |
dc.contributor.author | Tan, B.P. | |
dc.date.accessioned | 2014-10-28T02:41:12Z | |
dc.date.available | 2014-10-28T02:41:12Z | |
dc.date.issued | 2006-11-06 | |
dc.identifier.citation | Tan, B.P. (2006-11-06). On the 3-kings and 4-kings in multipartite tournaments. Discrete Mathematics 306 (21) : 2702-2710. ScholarBank@NUS Repository. https://doi.org/10.1016/j.disc.2006.04.023 | |
dc.identifier.issn | 0012365X | |
dc.identifier.uri | http://scholarbank.nus.edu.sg/handle/10635/103765 | |
dc.description.abstract | 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) 281-287, K.M. Koh, B.P. Tan, The number of kings in a multipartite tournament, Discrete Math. 167/168 (1997) 411-418] Koh and Tan showed that in any n-partite tournament with no transmitters and 3-kings, where n ≥ 2, the number of 4-kings is at least eight, and completely characterized all n-partite tournaments having exactly eight 4-kings and no 3-kings. Using Theorem 1, we strengthen substantially the above result for n ≥ 3. Motivated by the strengthened result, we further show that in any n-partite tournament T with no transmitters and 3-kings, where n ≥ 3, if there are r partite sets of T which contain 4-kings, where 3 ≤ r ≤ n, then the number of 4-kings in T is at least r + 8. An example is given to justify that the lower bound is sharp. © 2006 Elsevier B.V. All rights reserved. | |
dc.description.uri | http://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/j.disc.2006.04.023 | |
dc.source | Scopus | |
dc.subject | Distances | |
dc.subject | Kings | |
dc.subject | Multipartite tournaments | |
dc.type | Article | |
dc.contributor.department | MATHEMATICS | |
dc.description.doi | 10.1016/j.disc.2006.04.023 | |
dc.description.sourcetitle | Discrete Mathematics | |
dc.description.volume | 306 | |
dc.description.issue | 21 | |
dc.description.page | 2702-2710 | |
dc.description.coden | DSMHA | |
dc.identifier.isiut | 000241486400007 | |
Appears in Collections: | Staff Publications |
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