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- W3204127902 abstract "Following on the King Chicken Theorems originally proved by Maurer, we examine the idea of multiple flocks of chickens by bringing the chickens from tournaments to multipartite tournaments. As Kings have already been studied in multipartite settings, notably by Koh-Tan and Petrovic-Thomassen, we examine a new type of chicken more suited than Kings for these multipartite graphs: Dukes. We define an M-Duke to be a vertex from which any vertex in a different partite set is accessible by a directed path of length at most M. In analogy with Maurer's paper, we prove various structural results regarding Dukes. In particular, we prove the existence of 3-Dukes in all multipartite tournaments, and we conclude by proving that in any multipartite tournament, either there is a 1-Duke, three 2-Dukes, or four 3-Dukes." @default.
- W3204127902 created "2021-10-11" @default.
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- W3204127902 date "2021-09-28" @default.
- W3204127902 modified "2023-09-27" @default.
- W3204127902 title "Chickens and Dukes." @default.
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