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On random graphs, I
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A combinatorial problem in geometry
Our present problem has been suggested by Miss Esther Klein in connection with the following proposition.
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2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the setExpand
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On an extremal problem in graph theory
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Some remarks on the theory of graphs
The present note consists of some remarks on graphs. A graph G is a set of points some of which are connected by edges. We assume here that no two points are connected by more than one edge. TheExpand
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On Sets of Distances of n Points
1. The function f(n). Let [P. ] be the class of all planar subsets P. of n points and denote by f(n) the minimum number of different distances determined by its n points for P,, an element of { P. }.Expand
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On a lemma of Littlewood and Offord
Remark. Choose Xi = l, n even. Then the interval ( — 1, + 1 ) contains Cn,m s u m s ^ i e ^ , which shows that our theorem is best possible. We clearly can assume that all the Xi are not less than 1.Expand
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Graph Theory and Probability
A well-known theorem of Ramsay (8; 9) states that to every n there exists a smallest integer g(n) so that every graph of g(n) vertices contains either a set of n independent points or a completeExpand
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On extremal problems of graphs and generalized graphs
AbstractAnr-graph is a graph whose basic elements are its vertices and r-tuples. It is proved that to everyl andr there is anε(l, r) so that forn>n0 everyr-graph ofn vertices andnr−ε(l, r) r-tuplesExpand
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Ramsey-type theorems
In this paper we will consider Ramsey-type problems for finite graphs, r -partitions and hypergraphs. Expand
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