منابع مشابه
t-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 کاملLandau's inequalities for tournament scores and a short proof of a theorem on transitive sub-tournaments
Ao and Hanson, and Guiduli, Gy arf as, Thomass e and Weidl independently, proved the following result: For any tournament score sequence S = (s1; s2; : : : ; sn) with s1 s2 sn, there exists a tournament T on vertex set f1; 2; : : :; ng such that the score of each vertex i is si and the sub-tournaments of T on both the even and the odd indexed vertices are transitive in the given order; that is,...
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 کاملOn Convex Subsets in Tournaments
A tournament is a complete directed graph. A convex subset is a vertex subset with the property that every two-path beginning and ending inside the convex subset is contained completely within the subset. This paper shows that every nontrivial convex subset is the closure of a subset of vertices of cardinality two. This result leads to algorithms that nd all convex subsets in a tournament in O(...
متن کاملA 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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ژورنال
عنوان ژورنال: Acta Universitatis Sapientiae, Informatica
سال: 2018
ISSN: 2066-7760
DOI: 10.2478/ausi-2018-0013