منابع مشابه
Dominating sets in k-majority tournaments
A k-majority tournament T on a finite vertex set V is defined by a set of 2k − 1 linear orderings of V , with u→ v if and only if u lies above v in at least k of the orders. Motivated in part by the phenomenon of “non-transitive dice”, we let F (k) be the maximum over all k-majority tournaments T of the size of a minimum dominating set of T . We show that F (k) exists for all k > 0, that F (2) ...
متن کاملAcyclic Sets in k-Majority Tournaments
When Π is a set of k linear orders on a ground set X, and k is odd, the k-majority tournament generated by Π has vertex set X and has an edge from u to v if and only if a majority of the orders in Π rank u before v. Let fk(n) be the minimum, over all k-majority tournaments with n vertices, of the maximum order of an induced transitive subtournament. We prove that f3(n) ≥ √ n always and that f3(...
متن کاملA Recurrence for Bounds on Dominating Sets in k-Majority Tournaments
A k-majority tournament is realized by 2k−1 linear orders on the set of vertices, where a vertex u dominates v if u precedes v in at least k of the orders. Various properties of such tournaments have been studied, among them the problem of finding the size of a smallest dominating set. It is known that 2-majority tournaments are dominated by 3 vertices and that k-majority tournaments are domina...
متن کاملRepresentation in majority tournaments
The paper presents a general setting for studying majority-based collective decision procedures where the electorate is divided into constituencies according to an equal-representation principle. It generalizes the well-known Referendum Paradox to the non-dichotomous choice case, and shows that all Condorcet choice rules are sensitive to the design of the apportionment of the electorate, in the...
متن کاملOn non-z(mod k) dominating sets
For a graph G, a positive integer k, k ≥ 2, and a non-negative integer with z < k and z 6= 1, a subset D of the vertex set V (G) is said to be a non-z (mod k) dominating set if D is a dominating set and for all x ∈ V (G), |N [x] ∩ D| 6≡ z (mod k). For the case k = 2 and z = 0, it has been shown that these sets exist for all graphs. The problem for k ≥ 3 is unknown (the existence for even values...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2006
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2005.09.003