On a lower bound for the connectivity of the independence complex of a graph

Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false. ► The connectivity of the independence...

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Bibliographic Details
Published inDiscrete mathematics Vol. 311; no. 21; pp. 2566 - 2569
Main Authors Adamaszek, Michał, Barmak, Jonathan Ariel
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 06.11.2011
Elsevier
Subjects
Algebra
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Graphs
Independence complex
Information retrieval. Graph
Lower bounds
Mathematical analysis
Mathematics
Optimization
Sciences and techniques of general use
Theoretical computing
Topological connectivity
Independence complex
Topological connectivity
Lower bound
Graph connectivity
Independence
Discrete mathematics
Combinatorics
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Summary:Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false. ► The connectivity of the independence complex of a graph is studied. ► We provide an explicit proof of a lower bound proposed by Aharoni, Berger and Ziv. ► The conjecture that this bound is always an equality is disproved. ► Explicit counterexamples to the conjecture are constructed.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0012-365X
1872-681X
1872-681X
DOI:10.1016/j.disc.2011.06.010