Non-Bipartite K-Common Graphs

被引：5

作者：

Kral, Daniel ^{[1
,2
,3
]}

Noel, Jonathan A. ^{[2
,4
,5
,6
]}

Norin, Sergey ^{[7
]}

Volec, Jan ^{[1
,8
]}

Wei, Fan ^{[9
,10
]}

机构：

[1] Masaryk Univ, Fac Informat, Botanicka 68A, Brno 60200, Czech Republic

[2] Univ Warwick, Math Inst, DIMAP, Coventry CV4 7AL, W Midlands, England

[3] Univ Warwick, Dept Comp Sci, Coventry CV4 7AL, W Midlands, England

[4] Univ Victoria, Dept Math & Stat, David Turpin Bldg A425,3800 Finnerty Rd, Victoria, BC V8P 5C2, Canada

[5] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

[6] Univ Warwick, DIMAP, Coventry CV4 7AL, W Midlands, England

[7] McGill Univ, Dept Math & Stat, Montreal, PQ, Canada

[8] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Dept Math, Trojanova 13, Prague 12000, Czech Republic

[9] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[10] Inst Adv Study, Sch Math, Princeton, NJ USA

来源：

COMBINATORICA | 2022年 / 42卷 / 01期

基金：

加拿大自然科学与工程研究理事会; 欧洲研究理事会;

关键词：

05C55; 05C35; MULTIPLICITIES; CONJECTURE;

D O I：

10.1007/s00493-020-4499-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K-n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason [20]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko.

引用

页码：87 / 114

页数：28

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