A combinatorial problem in geometry
P. Erdös,G. Szekeres +1 more
TLDR
In this paper, the present problem has been suggested by Miss Esther Klein in connection with the following proposition: "Our present problem is the same problem as the one suggested by the author of this paper."Abstract:
Our present problem has been suggested by Miss Esther Klein in connection with the following proposition.read more
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Book ChapterDOI
Graph Theory and Probability
TL;DR: A well-known theorem of Ramsay (8, 9) states that to every n there exists a smallest integer g(n) such that every graph of g n contains either a set of n independent points or a complete graph of order n.
Book ChapterDOI
Art Gallery and Illumination Problems
TL;DR: Since Victor Klee's question, numerous variations on the art gallery problem have been studied, including mobile guards, guards with limited visibility or mobility, illumination of families of convex sets on the plane, guarding of rectilinear polygons, and others.
Geometric Range Searching and Its Relatives
Pankaj K. Agarwal,Je Erickson +1 more
TL;DR: This volume provides an excellent opportunity to recapitulate the current status of geometric range searching and to summarize the recent progress in this area.
Journal ArticleDOI
Graph minors. XVI. excluding a non-planar graph
Neil Robertson,Paul Seymour +1 more
TL;DR: It is found that every graph with no minor isomorphic to L may be constructed by piecing together in a tree-structure graphs each of which "almost" embeds in some surface in which L cannot be embedded.
Journal ArticleDOI
A Partition Calculus in Set Theory
Paul Erdös,Richard Rado +1 more
TL;DR: The Chest of Drawers argument as mentioned in this paper is an extension of the pigeon-hole principle, which was first introduced by Dedekind in the early 1970s, and it can be expressed as follows: if sufficiently many objects are distributed over not too many classes, then at least one class contains many of these objects.