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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.
INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
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 set
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. The
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.
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. }.
On extremal problems of graphs and generalized graphs
  • P. Erdös
  • Mathematics, Computer Science
  • 1 September 1964
TLDR
It is proved that to everyl andr there is anε(l, r) so that forn>n0 everyr-graph ofn vertices andnr−ε( l, r), which means that all ther-tuples occur in ther-graph.
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 complete
Some Problems on Random Walk in Space
Consider the lattice formed by all points whose coordinates are integers in d-dimensional Euclidean space, and let a point S j(n) perform a move randomly on this lattice according to the following
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