Erdős on Unit Distances and the Szemerédi-Trotter Theorems

Erdős on Unit Distances and the Szemerédi-Trotter Theorems

Cached

Download Links

[www.math.sc.edu]
[www.math.sc.edu]

Other Repositories/Bibliography

DBLP

by László A. Székely

Citations:

2 - 0 self

BibTeX

@MISC{Székely_erdőson,
    author = {László A. Székely},
    title = {Erdős on Unit Distances and the Szemerédi-Trotter Theorems},
    year = {}
}

Bookmark

OpenURL

Abstract

This is a concise review that attempts to show the vast influence of the work of Paul Erdős in a narrow area, the combinatorics of unit distances in geometry. This review tries to follow the history of the problems and cover the latest and strongest results, but cannot be complete. Excellent

Citations

147	Combinatorial Geometry - Pach, Agarwal - 1995
136	Combinatorial complexity bounds for arrangements of curves and spheres, Discrete and Computational Geometry 5 - Clarkson, Edelsbrunner, et al. - 1990
117	Kneser’s conjecture, chromatic number, and homotopy - Lovász - 1978
111	Intersection theorems with geometric consequences - Frankl, Wilson - 1981
99	On sets of distances of n points - Erdős - 1970
88	Complexity Issues in VLSI - Leighton - 1983
65	Research problems in discrete geometry - Moser
60	Crossing number problems - Erdős, Guy - 1973
52	On the chromatic number of graphs and set-systems - Erdős, Hajnal
41	Drei Satze uber die n-dimensionale euklidische Sphare - Borsuk - 1933
32	On the lattice property of the plane and some problems of Dirac - Beck - 1983
31	Extremal problems in combinatorial geometry - Erdős, Purdy - 1995
30	A counterexample to Borsuk's conjecture - Kahn, Kalai - 1993
28	Algebra Methods in Combinatorics - Babai, Frankl, et al. - 1992
26	On the number of incidences between points and curves - Pach, Sharir - 1998
24	On the dierent distances determined by n points - Moser - 1952
14	Solution to problem 10 - Moser, Moser - 1961
13	A problem of Leo Moser about repeated distances on the sphere, American Mathematical Monthly 96 - Erdos, Hickerson, et al. - 1989
12	Problems and results in combinatorial geometry - Erdos - 1985
11	A note on the realization of distances within sets in Euclidean - Larman - 1978
9	On Sets of Distances on n Points in Euclidean Space - Erdos - 1960
9	Self-dual polytopes and the chromatic number of distance graphs on the sphere - Lovasz - 1983
8	The realization of distances in measurable subsets covering - Falconer - 1981
6	A high girth 4-chromatic unit distance graph in the plane, talk at the Thirtieth - O'Donnell - 1999
5	Unit distances - Beck, Spencer
5	A Szemeredi-type theorem for sets of positive density - Bourgain
4	A colour problem for in graphs and a problem the theory of relations - Bruijn, Erdos - 1951
4	On dense bipartite graphs of girth eight and upper bounds for certain con in planar point-line systems - Caen, Szekely
4	On the number of dierent distances determined by n points in the plane - Chung
4	The number of dierent distances determined by a set of points in the Euclidean plane, Discrete Comp. Geometry 7 - Chung, Szemeredi, et al. - 1992
4	An 18-colouring of 3-space omitting distance one - Coulson
4	Incidence incidents - Croft - 1967
4	A Szemeredi{Trotter theorem on the complex plane, in preparation - Elekes, Toth
3	Crossing numbers of graphs, in: Graph Theory and its - Guy - 1972
3	A certain constructive estimate of the Ramsey number (Hungarian - Nagy - 1972
2	On some of my favourite theorems, Combinatorics, Paul Erd}os is Eighty (Volume 2 - Erdos - 1996
2	The realization of small distances in plane sets of positive measure - Falconer
1	On the maximum number of unit distances among n points in dimension four, Intuitive geometry - Bra - 1995
1	A 4-chromatic unit-distance graph with no triangles - Chilakamarri - 1995
1	A triangle-free 4-chromatic graph in the plane, Geombinatorics 4 - O'Donnell - 1994
1	Plane sets of positive density at in contain all large distances - Falconer, Marstrand
1	Traces of sets: extremal problems and geometric applications, in: Extremal Problems for Finite Sets, Visegrad - Furedi, Pach - 1991
1	Ergodic theory and con in sets of positive density - Furstenberg, Katznelson, et al. - 1990
1	Ein Uberdeckungsatz fur den Euklideschen - Hadwiger - 1944
1	Ungeloste Probleme No. 40, Elemente der Math 16 - Hadwiger - 1961
1	The number of unit distances on the plane, in: In and Finite - Jozsa, Szemeredi
1	An estimate in Borsuk's problem - Raigorodskii - 1999
1	The realization of all distances in a decomposition of IR n into n+1 parts - Raiskii - 1970