منابع مشابه
On High-Dimensional Acyclic Tournaments
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-...
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 کاملk-Colour Partitions of Acyclic Tournaments
Let G1 be the acyclic tournament with the topological sort 0 < 1 < 2 < · · · < n < n + 1 defined on node set N ∪ {0, n + 1}, where N = {1, 2, . . . , n}. For integer k ≥ 2, let Gk be the graph obtained by taking k copies of every arc in G1 and colouring every copy with one of k different colours. A k-colour partition of N is a set of k paths from 0 to n + 1 such that all arcs of each path have ...
متن کاملInduced acyclic tournaments in random digraphs: Sharp concentration, thresholds and algorithms
Given a simple directed graph D = (V,A), let the size of the largest induced acyclic tournament be denoted by mat(D). Let D ∈ D(n, p) (with p = p(n)) be a random instance, obtained by randomly orienting each edge of a random graph drawn from G(n, 2p). We show that mat(D) is asymptotically almost surely (a.a.s.) one of only 2 possible values, namely either b∗ or b∗ + 1, where b∗ = ⌊2(log r n) + ...
متن کاملA classification of tournaments having an acyclic tournament as a minimum feedback arc set
Given a tournament with an acyclic tournament as a feedback arc set we give necessary and sufficient conditions for this feedback arc set to have minimum size.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2019
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2019.04.007