Ramsey-Turan theory

被引：52
作者：
Simonovits, M [1 ]
Sós, VT [1 ]
机构：
[1] Hungarian Acad Sci, Inst Math, H-1364 Budapest, Hungary
来源：
DISCRETE MATHEMATICS | 2001年 / 229卷 / 1-3期
关键词：
graphs; hypergraphs; Ramsey theory; Turan-type extremal graph theory; Ramsey-Turan theorems; geometry;
D O I：
10.1016/S0012-365X(00)00214-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Ramsey- and Turan-type problems were always strongly related to each other. Motivated by an observation of Paul Erdos, it was Turan who started the systematic investigation of the applications of extremal graph theory in geometry and analysis. This led the second author to some results and problems which, in turn, led to the birth of Ramsey-Turan-type theorems. Today this is a wide field of research with many interesting results and many unsolved problems. Below we give a short survey of the most important parts of this field: starting with a historical sketch we continue by describing the Ramsey-Turan-type problems and results. Related problems in Ramsey theory. Some applications. (C) 2001 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：293 / 340
页数：48
相关论文
共 154 条
[91]  
KATONA G, 1969, MAT LAPOK, V20, P123
[92]  
KATONA G, 1980, DOKL AKAD NAUK SSSR, V251, P1293
[93]  
Katona G. O. H., 1981, European Journal of Combinatorics, V2, P145
[94]   BEST ESTIMATIONS ON THE DISTRIBUTION OF THE LENGTH OF SUMS OF 2 RANDOM VECTORS [J].
KATONA, GOH .
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1982, 60 (03) :411-423
[95]  
KATONA GOH, 1985, ANN DISCRETE MATH, V28, P159
[96]   THE RAMSEY NUMBER R(3,T) HAS ORDER OF MAGNITUDE T(2)/LOG-T [J].
KIM, JH .
RANDOM STRUCTURES & ALGORITHMS, 1995, 7 (03) :173-207
[97]   Norm-graphs and bipartite Turan numbers [J].
Kollar, J ;
Ronyai, L ;
Szabo, T .
COMBINATORICA, 1996, 16 (03) :399-406
[98]  
KOMLOS J, 1982, J LOND MATH SOC, V25, P13
[99]  
KOMLOS J, 1981, J LOND MATH SOC, V24, P385
[100]  
KOMLOS J, 1993, P C BOL MATH SOC KEZ, V2
567891011121314