Nearly-linear monotone paths in edge-ordered graphs

被引：7

作者：

Bucic, Matija ^{[1
]}

Kwan, Matthew ^{[2
]}

Pokrovskiy, Alexey ^{[3
]}

Sudakov, Benny ^{[1
]}

Tran, Tuan ^{[4
]}

Wagner, Adam Zsolt ^{[1
]}

机构：

[1] Swiss Fed Inst Technol, Dept Math, CH-8092 Zurich, Switzerland

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[3] Birkbeck Univ London, Dept Econ Math & Stat, London WC1E 7HX, England

[4] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, Hanoi, Vietnam

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2020年 / 238卷 / 02期

关键词：

EXTREMAL COMBINATORICS; REGULAR SUBGRAPHS; ALTITUDE;

D O I：

10.1007/s11856-020-2035-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

How long a monotone path can one always find in any edge-ordering of the complete graphK(n)? This appealing question was first asked by Chvatal and Komlos in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound wasn(2/3-o(1)). In this paper we almost close this gap, proving that any edge-ordering of the complete graph contains a monotone path of lengthn(1-o(1)).

引用

页码：663 / 685

页数：23

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