Pancyclic out-arcs of a vertex in tournaments
نویسندگان
چکیده
منابع مشابه
Pancyclic out-arcs of a Vertex in Tournaments
Thomassen (J. Combin. Theory Ser. B 28, 1980, 142–163) proved that every strong tournament contains a vertex x such that each arc going out from x is contained in a Hamiltonian cycle. In this paper, we extend the result of Thomassen and prove that a strong tournament contains a vertex x such that every arc going out from x is pancyclic, and our proof yields a polynomial algorithm to nd such a v...
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Let $T$ be a non-trivial tournament. An arc is emph{$t$-pancyclic} in $T$, if it is contained in a cycle of length $ell$ for every $tleq ell leq |V(T)|$. Let $p^t(T)$ denote the number of $t$-pancyclic arcs in $T$ and $h^t(T)$ the maximum number of $t$-pancyclic arcs contained in the same Hamiltonian cycle of $T$. Moon ({em J. Combin. Inform. System Sci.}, {bf 19} (1994), 207-214) showed that $...
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A k-hypertournament H on n vertices, where 2 ≤ k ≤ n, is a pair H = (V,AH), where V is the vertex set of H and AH is a set of k-tuples of vertices, called arcs, such that for all subsets S ⊆ V of order k, AH contains exactly one permutation of S as an arc. Inspired by the successful extension of classical results for tournaments (i.e. 2-hypertournaments) to hypertournaments, by Gutin and Yeo [J...
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An arc in a tournament T with n ≥ 3 vertices is called pancyclic if it belongs to a cycle of length l for all 3 ≤ l ≤ n. We call a vertex u of T an out-arc pancyclic vertex of T if each out-arc of u is pancyclic in T . Yao, Guo and Zhang [Discrete Appl. Math. 99 (2000), 245–249] proved that every strong tournament contains at least one out-arc pancyclic vertex, and they gave an infinite class o...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2000
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(99)00136-5