Oriented Hamiltonian Paths in Tournaments: A Proof of Rosenfeld's Conjecture
نویسندگان
چکیده
منابع مشابه
On the oriented perfect path double cover conjecture
An oriented perfect path double cover (OPPDC) of a graph $G$ is a collection of directed paths in the symmetric orientation $G_s$ of $G$ such that each arc of $G_s$ lies in exactly one of the paths and each vertex of $G$ appears just once as a beginning and just once as an end of a path. Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete Math. 276 (2004) 287-294) conjectured that ...
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Solving an old conjecture of Szele we show that the maximum number of directed Hamiltonian paths in a tournament on n vertices is at most c · n · n! 2n−1 , where c is a positive constant independent of n.
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Sufficient conditions are given for the existence of an oriented path with given end vertices in a tournament. As a consequence a conjecture of Rosenfeld is established. This states that if n is large enough, then every non-strongly oriented cycle of order n is contained in every tournament of order n. It is well known and easy to see that every tournament has a directed hamilton path. Rosenfel...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 78 شماره
صفحات -
تاریخ انتشار 2000