Covering the edges of a graph with triangles

被引：0

作者：

Bujtas, Csilla ^{[1
,2
,3
]}

Davoodi, Akbar ^{[4
]}

Ding, Laihao ^{[5
,6
]}

Gyori, Ervin ^{[7
,9
]}

Tuza, Zsolt ^{[8
,9
]}

Yang, Donglei ^{[10
]}

机构：

[1] Univ Ljubljana, Ljubljana, Slovenia

[2] Inst Math Phys & Mech, Ljubljana, Slovenia

[3] Univ Pannonia, Veszprem, Hungary

[4] Czech Acad Sci, Inst Comp Sci, Vodarenskou vezi 2, Prague 18207, Czech Republic

[5] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China

[6] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China

[7] Cent European Univ, Budapest, Hungary

[8] Univ Pannonia, Dept Comp Sci & Syst Technol, Veszprem, Hungary

[9] HUN REN Alfred Reny Inst Math, Budapest, Hungary

[10] Shandong Univ, Sch Math, Jinan, Peoples R China

来源：

DISCRETE MATHEMATICS | 2025年 / 348卷 / 01期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Edge-disjoint triangles; Edge clique covering; Nordhaus-Gaddum inequality;

D O I：

10.1016/j.disc.2024.114226

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a graph G, let rho(Delta)(G) denote the minimum size of a set of edges and triangles that cover all edges of G, and let alpha(1)(G) be the maximum size of an edge set that contains at most one edge from each triangle. Motivated by a question of Erdos, Gallai, and Tuza, we study the relationship between rho(Delta)(G) and alpha(1)(G) and establish a sharp upper bound on rho(Delta)(G). We also prove Nordhaus-Gaddum-type inequalities for the considered invariants. (c) 2024 The Author(s).

引用

页数：8

共 50 条

[31] Covering a Convex Polygon by Triangles
András Bezdek
Geometriae Dedicata, 2000, 80 : 73 - 79
[32] Packing and Covering Directed Triangles
Jessica McDonald
Gregory J. Puleo
Craig Tennenhouse
Graphs and Combinatorics, 2020, 36 : 1059 - 1063
[33] Covering a convex polygon by triangles
Bezdek, A
GEOMETRIAE DEDICATA, 2000, 80 (1-3) : 73 - 79
[34] On a covering problem for equilateral triangles
Dumitrescu, Adrian
Jiang, Minghui
ELECTRONIC JOURNAL OF COMBINATORICS, 2008, 15 (01):
[35] Packing and covering triangles in graphs
Discrete Math, 1-3 (251-254):
[36] On the Multiple Covering Densities of Triangles
Kirati Sriamorn
Akanat Wetayawanich
Discrete & Computational Geometry, 2015, 54 : 717 - 727
[37] Packing and covering triangles in graphs
Haxell, PE
DISCRETE MATHEMATICS, 1999, 195 (1-3) : 251 - 254
[38] COVERING EDGES BY CLIQUES
BRODER, AZ
COMMUNICATIONS OF THE ACM, 1979, 22 (05) : 312 - 312
[39] Covering edges in networks
Froehlich, Nicolas
Maier, Andrea
Hamacher, Horst W.
NETWORKS, 2020, 75 (03) : 278 - 290
[40] Counting Triangles in Real-World Graph Streams: Dealing with Repeated Edges and Time Windows
Jha, Madhav
Pinar, Ali
Seshadhri, C.
2015 49TH ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS AND COMPUTERS, 2015, : 1507 - 1514

← 1 2 3 4 5 →