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

共 50 条

[1] SHARP BOUNDS FOR DECOMPOSING GRAPHS INTO EDGES AND TRIANGLES
Blumenthal, A.
Lidicky, B.
Pikhurko, O.
Pehova, Y.
Pfender, F.
Volec, J.
[J]. ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2019, 88 (03): : 463 - 468
[2] Sharp bounds for decomposing graphs into edges and triangles
Blumenthal, Adam
Lidicky, Bernard
Pehova, Yanitsa
Pfender, Florian
Pikhurko, Oleg
Volec, Jan
[J]. COMBINATORICS PROBABILITY & COMPUTING, 2021, 30 (02): : 271 - 287
[3] Decomposing subcubic graphs into claws, paths or triangles
Bulteau, Laurent
Fertin, Guillaume
Labarre, Anthony
Rizzi, Romeo
Rusu, Irena
[J]. JOURNAL OF GRAPH THEORY, 2021, 98 (04) : 557 - 588
[4] Decomposing toroidal graphs into circuits and edges
Xu, BG
Wang, LS
[J]. DISCRETE APPLIED MATHEMATICS, 2005, 148 (02) : 147 - 159
[5] On light edges and triangles in projective planar graphs
Sanders, DP
[J]. JOURNAL OF GRAPH THEORY, 1996, 21 (03) : 335 - 342
[6] Decomposing Random Graphs into Few Cycles and Edges
Korandi, Daniel
Krivelevich, Michael
Sudakov, Benny
[J]. COMBINATORICS PROBABILITY & COMPUTING, 2015, 24 (06): : 857 - 872
[7] Contractible edges and triangles in k-connected graphs
Kawarabayashi, K
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2002, 85 (02) : 207 - 221
[8] On the Number of Edges in Geometric Graphs Without Empty Triangles
Bautista-Santiago, C.
Heredia, M. A.
Huemer, C.
Ramirez-Vigueras, A.
Seara, C.
Urrutia, J.
[J]. GRAPHS AND COMBINATORICS, 2013, 29 (06) : 1623 - 1631
[9] On the Number of Edges in Geometric Graphs Without Empty Triangles
C. Bautista-Santiago
M. A. Heredia
C. Huemer
A. Ramírez-Vigueras
C. Seara
J. Urrutia
[J]. Graphs and Combinatorics, 2013, 29 : 1623 - 1631
[10] Using shortcut edges to maximize the number of triangles in graphs
Dehghani, Sina
Fazli, Mohammad Amin
Habibi, Jafar
Yazdanbod, Sadra
[J]. OPERATIONS RESEARCH LETTERS, 2015, 43 (06) : 586 - 591

← 1 2 3 4 5 →