منابع مشابه
Ramsey Graphs and Block Designs
This paper establishes a connection between a certain class of Ramsey numbers for graphs and the class of symmetric block designs admitting a polarity. The main case considered here relates the projective planes over Galois fields to the Ramsey numbers R(Ca, Kx „) = f(n). It is shown that, for 2 2 ' 2 2 every prime power q, f(q + 1) = q + q + 2, and f(q ) = q + q + 1.
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Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by ...
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We prove that for any choice of parameters k, t, λ the class of all finite ordered designs with parameters k, t, λ is a Ramsey class.
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Given a combinatorial designD with block set B, its traditional block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and only if b1 and b2 have non-empty intersection. In this paper we consider the S-block-intersection graph, in which two vertices b1 and b2 are adjacent if and only if |b1 ∩ b2| ∈ S. As our main result we prove that {1, 2,...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1976
ISSN: 0097-3165
DOI: 10.1016/0097-3165(76)90074-1