Domination in tournaments
نویسندگان
چکیده
منابع مشابه
Domination in tournaments
We investigate the following conjecture of Hehui Wu: for every tournament S, the class of S-free tournaments has bounded domination number. We show that the conjecture is false in general, but true when S is 2-colourable (that is, its vertex set can be partitioned into two transitive sets); the latter follows by a direct application of VC-dimension. Our goal is to go beyond this; we give a non-...
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A set S ⊆ V of vertices in a graph G = (V,E) is called a dominating set if every vertex in V − S is adjacent to at least one vertex in S. Domination in graphs is a well-studied branch of graph theory, and is the subject of two books by Haynes, Hedetniemi and Slater [8, 9]. However, about 90% of the papers on domination have considered only undirected graphs. Thus, relatively little is known abo...
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The definition for the domination graph of a tournament states that it has the same vertices as the tournament with an edge between two vertices if every other vertex is beaten by at least one of them. In this paper two generalisations of domination graphs are proposed by using different relaxations of the adjacency definition. The first type is formed by reducing the number of vertices which m...
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An edge coloring of a tournament T with colors 1, 2, . . . , k is called ktransitive if the digraph T (i) defined by the edges of color i is transitively oriented for each 1 ≤ i ≤ k. We explore a conjecture of the first author: For each positive integer k there exists a (least) p(k) such that every k-transitive tournament has a dominating set of at most p(k) vertices. We show how this conjectur...
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The domination graph of a digraph has the same vertices as the digraph with an edge between two vertices if every other vertex loses to at least one of the two. Previously, the authors showed that the domination graph of a tournament is either an odd cycle with or without isolated and/or pendant vertices, or a forest of caterpillars. They also showed that any graph consisting of an odd cycle wi...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2018
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2017.10.001