منابع مشابه
All Triangles Are Ramsey
Given a triangle ABC and an integer r, r > 2, it is shown that for n sufficiently large and an arbitrary r-coloring of Rn one can find a monochromatic copy of ABC.
متن کاملAll Ramsey (2K2,C4)−Minimal Graphs
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 ...
متن کاملHypergraph Ramsey numbers: Triangles versus cliques
A celebrated result in Ramsey Theory states that the order of magnitude of the trianglecomplete graph Ramsey numbers R(3, t) is t/ log t. In this paper, we consider an analogue of this problem for uniform hypergraphs. A triangle is a hypergraph consisting of edges e, f, g such that |e∩ f | = |f ∩ g| = |g ∩ e| = 1 and e ∩ f ∩ g = ∅. For all r ≥ 2, let R(C3,K t ) be the smallest positive integer ...
متن کاملMetric Spaces in which All Triangles Are Degenerate Bettina
In any subspace of the real line R with the usual Euclidean metric d(x, y) = |x− y|, every triangle is degenerate. In R or R with the usual Euclidean metrics, a triangle is degenerate if and only if its vertices are collinear. With our intuition of a degenerate triangle having “collinear vertices” extended to arbitrary metric spaces, we might expect that a metric space in which every triangle i...
متن کاملCounting All Equilateral Triangles In
We describe a procedure of counting all equilateral triangles in the three dimensional space whose coordinates are allowed only in the set {0, 1, ..., n}. This sequence is denoted here by ET (n) and it has the entry A102698 in “The On-Line Encyclopedia of Integer Sequences”. The procedure is implemented in Maple and its main idea is based on the results in [3]. Using this we calculated the valu...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1986
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1986-0854099-6