An upper bound for the restricted online Ramsey number
نویسندگان
چکیده
منابع مشابه
An Upper Bound for the Ramsey Numbers
The Ramsey number r(H,G) is defined as the minimum N such that for any coloring of the edges of the N -vertex complete graph KN in red and blue, it must contain either a red H or a blue G. In this paper we show that for any graph G without isolated vertices, r(K3, G) ≤ 2q + 1 where G has q edges. In other words, any graph on 2q + 1 vertices with independence number at most 2 contains every (iso...
متن کاملAn upper bound for the Ramsey numbers r(&, G)*
The Ramsey number r(H, G) is defined as the minimum N such that for any coloring of the edges of the N-vertex complete graph KN in red and blue, it must contain either a ted H or a blue G. In this paper we show that for any graph G without isolated vertices, r(K,, G)< 2qf 1 where G has q edges. In other words, any graph on 2q+ 1 vertices with independence number at most 2 contains every (isolat...
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A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. The total domination number of a graph $G$, denoted by $gamma_t(G)$, is~the minimum cardinality of a total dominating set of $G$. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004), 6...
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We consider the following question: how large does n have to be to guarantee that in any two-colouring of the edges of the complete graph Kn,n there is a monochromatic Kk,k? In the late seventies, Irving [5] showed that it was sufficient, for k large, that n ≥ 2k−1(k−1)−1. Here we improve upon this bound, showing that it is sufficient to take n ≥ (1 + o(1))2 log k, where the log is taken to the...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.05.024