On the bounded domination number of tournaments
نویسندگان
چکیده
منابع مشابه
On the bounded domination number of tournaments
In a simple digraph, a star of degree t is a union of t edges with a common tail. The k-domination number k(G) of digraph G is the minimum number of stars of degree at most k needed to cover the vertex set. We prove that k(T )= dn=(k +1)e when T is a tournament with n¿14k lg k vertices. This improves a result of Chen, Lu and West. We also give a short direct proof of the result of E. Szekeres a...
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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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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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00029-7