An improved lower bound on the independence number of a graph

Michael A. Henning; Christian Löwenstein

doi:10.1016/j.dam.2014.07.001

An improved lower bound on the independence number of a graph

Michael A. Henning
, Christian Löwenstein

Mathematics and Applied Mathematics

Ulm University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The independence number of a graph G, denoted α(G), is the maximum cardinality of an independent set of vertices in G. Our main result is the strengthening of a lower bound for the independence number of a graph due to Löwenstein et al. (2011) who proved that if G is a connected graph of order n and size m, then α(G)≥23n-14m-13. We show that if G does not belong to a specific family of graphs, then α(G)>23n-14m. Further, we characterize the graphs G for which α(G)≤23n-14m.

Original language	English
Pages (from-to)	120-128
Number of pages	9
Journal	Discrete Applied Mathematics
Volume	179
DOIs	https://doi.org/10.1016/j.dam.2014.07.001
Publication status	Published - 31 Dec 2014

Keywords

Independence
Vertex-cover

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2014.07.001

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title = "An improved lower bound on the independence number of a graph",

abstract = "The independence number of a graph G, denoted α(G), is the maximum cardinality of an independent set of vertices in G. Our main result is the strengthening of a lower bound for the independence number of a graph due to L{\"o}wenstein et al. (2011) who proved that if G is a connected graph of order n and size m, then α(G)≥23n-14m-13. We show that if G does not belong to a specific family of graphs, then α(G)>23n-14m. Further, we characterize the graphs G for which α(G)≤23n-14m.",

keywords = "Independence, Vertex-cover",

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AU - Henning, Michael A.

AU - Löwenstein, Christian

PY - 2014/12/31

Y1 - 2014/12/31

N2 - The independence number of a graph G, denoted α(G), is the maximum cardinality of an independent set of vertices in G. Our main result is the strengthening of a lower bound for the independence number of a graph due to Löwenstein et al. (2011) who proved that if G is a connected graph of order n and size m, then α(G)≥23n-14m-13. We show that if G does not belong to a specific family of graphs, then α(G)>23n-14m. Further, we characterize the graphs G for which α(G)≤23n-14m.

AB - The independence number of a graph G, denoted α(G), is the maximum cardinality of an independent set of vertices in G. Our main result is the strengthening of a lower bound for the independence number of a graph due to Löwenstein et al. (2011) who proved that if G is a connected graph of order n and size m, then α(G)≥23n-14m-13. We show that if G does not belong to a specific family of graphs, then α(G)>23n-14m. Further, we characterize the graphs G for which α(G)≤23n-14m.

KW - Independence

KW - Vertex-cover

UR - https://www.scopus.com/pages/publications/84922256844

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DO - 10.1016/j.dam.2014.07.001

M3 - Article

AN - SCOPUS:84922256844

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SP - 120

EP - 128

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

An improved lower bound on the independence number of a graph

Abstract

Keywords

ASJC Scopus subject areas

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