منابع مشابه
Short Score Certificates for Upset Tournaments
A score certificate for a tournament, T , is a collection of arcs of T which can be uniquely completed to a tournament with the same scorelist as T ’s, and the score certificate number of T is the least number of arcs in a score certificate of T . Upper bounds on the score certificate number of upset tournaments are derived. The upset tournaments on n vertices are in one–to–one correspondence w...
متن کاملAsymptotic Enumeration of Tournaments with a Given Score Sequence
A tournament is a digraph in which, for each pair of distinct vertices v and w, either (v,w) or (w, v) is an edge, but not both. A tournament is regular if the in-degree is equal to the out-degree at each vertex. Let v1, v2, . . . , vn be the vertices of a labelled tournament and let d−j , d + j be the in-degree and out-degree of vj for 1 ≤ j ≤ n. d+j is also called the score of vj . Define δj ...
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...
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 $...
متن کامل5 S ep 2 00 6 SCORE SETS IN k - PARTITE TOURNAMENTS
The set S of distinct scores (outdegrees) of the vertices of a k-partite tournament T(X1, X2, · · · , X k) is called its score set. In this paper, we prove that every set of n non-negative integers, except {0} and {0, 1}, is a score set of some 3-partite tournament. We also prove that every set of n non-negative integers is a score set of some k-partite tournament for every n ≥ k ≥ 2.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1979
ISSN: 0095-8956
DOI: 10.1016/0095-8956(79)90045-5