On nonreconstructable tournaments
نویسندگان
چکیده
منابع مشابه
A Problem on Tournaments
By a tournament we mean the outcome of a round-robin tournament in which there are no draws . Such a tournament may be represented by a graph in which the n players are represented by vertices labelled 1, 2, . . . , n, and the outcomes of the games are represented by directed edges so that every pair of vertices is joined by one directed edge . We call such a graph a complete directed graph . O...
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We (re-)prove that in every 3-edge-coloured tournament in which no vertex is incident with all colours there is either a cyclic rainbow triangle or a vertex dominating every other vertex monochromatically.
متن کاملOn arc-traceable tournaments
A digraph D = (V, A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V , i.e. a hamiltonian path. Given a tournament T , it is well known that it contains a directed hamiltonian path. In this paper, we develop the structure necessary for a tournament T to contain an arc xy that is not on any hamiltonian path. Using this structure, we give suff...
متن کاملLocal Tournaments and In - Tournaments
Preface Tournaments constitute perhaps the most well-studied class of directed graphs. One of the reasons for the interest in the theory of tournaments is the monograph Topics on Tournaments [58] by Moon published in 1968, covering all results on tournaments known up to this time. In particular, three results deserve special mention: in 1934 Rédei [60] proved that every tournament has a directe...
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We study a high-dimensional analog for the notion of an acyclic (aka transitive) tournament. We give upper and lower bounds on the number of d-dimensional n-vertex acyclic tournaments. In addition, we prove that every n-vertex d-dimensional tournament contains an acyclic subtournament of (log1/d n) vertices and the bound is tight. This statement for tournaments (i.e., the case d = 1) is a well-...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1970
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(70)80088-6