Decomposing Graphs into Edges and Triangles

被引：8

作者：

Kral, Daniel ^{[1
,2
]}

Lidicky, Bernard ^{[3
]}

Martins, Taisa L. ^{[4
]}

Pehova, Yanitsa ^{[4
]}

机构：

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

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

[3] Iowa State Univ, Dept Math, Ames, IA 50011 USA

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

来源：

COMBINATORICS PROBABILITY & COMPUTING | 2019年 / 28卷 / 03期

基金：

英国工程与自然科学研究理事会; 欧洲研究理事会;

关键词：

INTEGER; DENSITY;

D O I：

10.1017/S0963548318000421

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove the following 30 year-old conjecture of Gyori and Tuza: the edges of every n-vertex graph G can be decomposed into complete graphs C-1, ..., C-l of orders two and three such that vertical bar C-1 vertical bar+ ... + vertical bar C-l vertical bar (1/2 + o(1))n(2). This result implies the asymptotic version of the old result of Erdos, Goodman and POsa that asserts the existence of such a decomposition with l <= n(2)/4.

引用

页码：465 / 472

页数：8

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