A new lower bound on the independence number of a graph and applications

被引：0

作者：

Henning, Michael A. ^{[1
]}

Loewenstein, Christian ^{[2
]}

Southey, Justin ^{[1
]}

Yeo, Anders ^{[1
,3
]}

机构：

[1] Univ Johannesburg, Dept Math, Auckland Pk, ZA-2006 Johannesburg, South Africa

[2] Univ Ulm, Inst Optimizat & Operat Res, D-89081 Ulm, Germany

[3] Singapore Univ Technol & Design, Singapore 138682, Singapore

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2014年 / 21卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

independence; clique; transversal; SMALL TRANSVERSALS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The independence number of a graph C, denoted a(G), is the maximum cardinality of an independent set of vertices in G. The independence number is one of the most fundamental and well-studied graph parameters. In this paper, we strengthen a result of Fajtlowicz [Combinatorica 4 (1984), 35-38] on the independence of a graph given its maximum degree and maximum clique size. As a consequence of our result we give bounds on the independence number and transversal number of 6-uniform hypergraphs with maximum degree three. This gives support for a conjecture due to Tuza and Vestergaard [Discussiones Math. Graph Theory 22 (2002), 199-210] that if H is a 3-regular 6-uniform hypergraph of order n, then T (H) <= n/4.

引用

页数：12

共 50 条

[21] A LOWER BOUND FOR THE INTERVAL NUMBER OF A GRAPH
MAAS, C
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1984, 10 (01) : 65 - 69
[22] A lower bound on the independence number of arbitrary hypergraphs
Thiele, T
JOURNAL OF GRAPH THEORY, 1999, 30 (03) : 213 - 221
[23] A new lower bound for the bipartite crossing number with applications
Shahrokhi, F
Sykora, O
Székely, LA
Vrt'o, I
THEORETICAL COMPUTER SCIENCE, 2000, 245 (02) : 281 - 294
[24] An inertial lower bound for the chromatic number of a graph
Elphick, Clive
Wocjan, Pawel
ELECTRONIC JOURNAL OF COMBINATORICS, 2017, 24 (01):
[25] A PROBABILISTIC LOWER-BOUND ON THE INDEPENDENCE NUMBER OF GRAPHS
SELKOW, SM
DISCRETE MATHEMATICS, 1994, 132 (1-3) : 363 - 365
[26] AN OPTIMAL LOWER BOUND ON THE NUMBER OF VARIABLES FOR GRAPH IDENTIFICATION
CAI, JY
FURER, M
IMMERMAN, N
COMBINATORICA, 1992, 12 (04) : 389 - 410
[27] A lower bound for secure domination number of an outerplanar graph
Araki, Toru
DISCRETE APPLIED MATHEMATICS, 2024, 357 : 81 - 85
[28] AN OPTIMAL LOWER BOUND ON THE NUMBER OF VARIABLES FOR GRAPH IDENTIFICATION
CAI, JY
FURER, M
IMMERMAN, N
30TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, 1989, : 612 - 617
[29] A lower bound for the CO-irredundance number of a graph
Finbow, S
DISCRETE MATHEMATICS, 2005, 295 (1-3) : 49 - 62
[30] Proof of a conjectured lower bound on the chromatic number of a graph
Ando, Tsuyoshi
Lin, Minghua
LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 485 : 480 - 484

← 1 2 3 4 5 →