PANCYCLIC ARCS IN HAMILTONIAN CYCLES OF HYPERTOURNAMENTS
نویسندگان
چکیده
منابع مشابه
Hamiltonian paths and cycles in hypertournaments
Given two integers n and k, n ≥ k > 1, a k-hypertournament T on n vertices is a pair (V, A), where V is a set of vertices, |V | = n and A is a set of k-tuples of vertices, called arcs, so that for any k-subset S of V , A contains exactly one of the k! k-tuples whose entries belong to S. A 2-hypertournament is merely an (ordinary) tournament. A path is a sequence v1a1v2a2v3...vt−1at−1vt of disti...
متن کاملt-Pancyclic Arcs in Tournaments
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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In [6], Thomassen conjectured that if I is a set of k − 1 arcs in a k-strong tournament T , then T − I has a Hamiltonian cycle. This conjecture was proved by Fraisse and Thomassen [3]. We prove the following stronger result. Let T = (V, A) be a k-strong tournament on n vertices and let X1, X2, . . . , Xl be a partition of the vertex set V of T such that |X1| ≤ |X2| ≤ . . . ≤ |Xl|. If k ≥ ∑l−1 i...
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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...
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...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2014
ISSN: 0304-9914
DOI: 10.4134/jkms.2014.51.6.1141