Making a tournament k-arc-strong by reversing or deorienting arcs
نویسندگان
چکیده
منابع مشابه
The 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 کاملSpanning k-arc-strong subdigraphs with few arcs in k-arc-strong tournaments
Given a k-arc-strong tournament T , we estimate the minimum number of arcs possible in a k-arc-strong spanning subdigraph of T . We give a construction which shows that for each k ≥ 2 there are tournaments T on n vertices such that every k-arc-strong spanning subdigraph of T contains at least nk+ k(k−1) 2 arcs. In fact, the tournaments in our construction have the property that every spanning s...
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u. and u . is joined by one of the (oriented) arcs u .u . or u.u . . 1 J 13 J 1 The arcs in some set S are said to be consistent if it is possible to relabel the nodes of the tournament in such a way that if the arc u.u . is in S then i > j . (This is easily seen to be equiva1 3 lent to requiring that the tournament contains no oriented cycles composed entirely of arcs of S . ) Sets of consiste...
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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 کاملCyclic Reversing K-symmetry Groups
We consider discrete invertible dynamical systems L with the property that the kth iterate L k possesses (reversing) symmetries that are not possessed by L. A map U is called a (reversing) k-symmetry of L if k is the smallest positive integer for which U is a (reversing) symmetry of L k. In this paper we discuss the particular case that L possesses a cyclic reversing k-symmetry group. We derive...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2004
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(03)00438-4