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

页码：293 / 340

页数：48

共 50 条

[31] Rainbow Generalizations of Ramsey Theory: A Survey [J].

Fujita, Shinya ;

Magnant, Colton ;

Ozeki, Kenta .

GRAPHS AND COMBINATORICS, 2010, 26 (01) :1-30

[32] The canonical Ramsey theorem and computability theory [J].

Mileti, Joseph R. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (03) :1309-1340

[33] Choiceless Ramsey Theory of Linear Orders [J].

Philipp Lücke ;

Philipp Schlicht ;

Thilo Weinert .

Order, 2017, 34 :369-418

[34] Rainbow Generalizations of Ramsey Theory: A Survey [J].

Shinya Fujita ;

Colton Magnant ;

Kenta Ozeki .

Graphs and Combinatorics, 2010, 26 :1-30

[35] On two problems in graph Ramsey theory [J].

Conlon, David ;

Fox, Jacob ;

Sudakov, Benny .

COMBINATORICA, 2012, 32 (05) :513-535

[36] Transitive sets in Euclidean Ramsey theory [J].

Leader, Imre ;

Russell, Paul A. ;

Walters, Mark .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2012, 119 (02) :382-396

[37] On generalized Ramsey theory:: The bipartite case [J].

Axenovich, M ;

Füredi, Z ;

Mubayi, D .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2000, 79 (01) :66-86

[38] Ramsey theory on generalized Baire space [J].

Hathaway, Dan .

TOPOLOGY AND ITS APPLICATIONS, 2018, 235 :104-112

[39] Discordant sets and ergodic Ramsey theory [J].

Bergelson, Vitaly ;

Huryn, Jake ;

Raghavan, Rushil .

INVOLVE, A JOURNAL OF MATHEMATICS, 2022, 15 (01) :89-130

[40] Rothberger bounded groups and Ramsey theory [J].

Scheepers, Marion .

TOPOLOGY AND ITS APPLICATIONS, 2011, 158 (13) :1575-1583

← 1 2 3 4 5 →