Independent domination in triangle-free graphs

Let G be a simple graph of order n and minimum degree δ . The independent domination number i ( G ) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. We establish upper bounds, as functions of n and δ ⩽ n / 2 , for the independent domination number of tria...

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Published inDiscrete mathematics Vol. 308; no. 16; pp. 3545 - 3550
Main Author Haviland, Julie
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 28.08.2008
Elsevier
Subjects
Algebra
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Independent domination
Mathematics
Sciences and techniques of general use
Triangle-free graphs
Independent domination
Triangle-free graphs
Upper bound
Domination number
Discrete mathematics
Independent set
Combinatorics
N order
Online AccessGet full text

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Abstract Let G be a simple graph of order n and minimum degree δ . The independent domination number i ( G ) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. We establish upper bounds, as functions of n and δ ⩽ n / 2 , for the independent domination number of triangle-free graphs, and over part of the range achieve best possible results.
AbstractList Let G be a simple graph of order n and minimum degree δ . The independent domination number i ( G ) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. We establish upper bounds, as functions of n and δ ⩽ n / 2 , for the independent domination number of triangle-free graphs, and over part of the range achieve best possible results.
Author Haviland, Julie
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Cites_doi 10.1016/0012-365X(88)90076-3
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Issue 16
Keywords Independent domination
Triangle-free graphs
Upper bound
Domination number
Discrete mathematics
Independent set
Combinatorics
N order
Language English
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Lam, Shiu, Sun (bib6) 1999; 202
Sun, Wang (bib7) 1999; 76
Favaron (bib1) 1988; 70
Haviland (bib2) 1991; 94
J. Haviland, Upper bounds for independent domination in regular graphs, Discrete Math. (2007), to appear, doi
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Haviland (bib3) 1995; 143
Sun (10.1016/j.disc.2007.07.010_bib7) 1999; 76
Lam (10.1016/j.disc.2007.07.010_bib6) 1999; 202
Haviland (10.1016/j.disc.2007.07.010_bib3) 1995; 143
Haynes (10.1016/j.disc.2007.07.010_bib5) 1998
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Favaron (10.1016/j.disc.2007.07.010_bib1) 1988; 70
Haviland (10.1016/j.disc.2007.07.010_bib2) 1991; 94
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SubjectTerms Algebra
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Independent domination
Mathematics
Sciences and techniques of general use
Triangle-free graphs
Title Independent domination in triangle-free graphs
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Volume 308
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