The number of vertices whose out-arcs are pancyclic in a 2-strong tournament
نویسندگان
چکیده
منابع مشابه
An s-strong tournament with s>=3 has s+1 vertices whose out-arcs are 4-pancyclic
An arc in a tournament T with n 3 vertices is called k-pancyclic, if it belongs to a cycle of length for all k n. In this paper, we show that each s-strong tournament with s 3 contains at least s + 1 vertices whose out-arcs are 4-pancyclic. © 2006 Elsevier B.V. All rights reserved.
متن کاملThe number of pancyclic arcs in a k-strong tournament
A tournament is a digraph, where there is precisely one arc between every pair of distinct vertices. An arc is pancyclic in a digraph D, if it belongs to a cycle of length l, for all 3 <= l <= |V (D)|. Let p(D) denote the number of pancyclic arcs in a digraph D and let h(D) denote the maximum number of pancyclic arcs belonging to the same Hamilton cycle of D. Note that p(D) >= h(D). Moon showed...
متن کاملThe out-arc 5-pancyclic vertices in strong tournaments
An arc in a tournament T with n ≥ 3 vertices is called k-pancyclic, if it belongs to a cycle of length l for all k ≤ l ≤ n. In this paper, the result that each s-strong (s ≥ 3) tournament T contains at least s + 2 out-arc 5-pancyclic vertices is obtained. Furthermore, our proof yields a polynomial algorithm to find s + 2 out-arc 5-pancyclic vertices of T .
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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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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2008
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.08.009