On local and global independence numbers of a graph

Authors:
Ralph J. Faudree;Zdeněk Ryjáček;Richard H. Schelp
Affiliations:
Department of Mathematical Sciences, The University of Memphis, Memphis, TN;Department of Mathematics, University of West Bohemia, Pilsen 306 14, Czech Republic and Institute of Theoretical Computer Science (ITI), Charles University, Pilsen 306 14, Czech Republic;Department of Mathematical Sciences, The University of Memphis, Memphis, TN
Venue:
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Year:
2003

Citing 4
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Abstract

The local independence number αi(G) of a graph G at a distance i is the maximum number of independent vertices at distance i from any vertex. We study the impact of restricting αi(G) on the (global) independence number α(G). Among others, we show that in graphs with bounded diameter, α(G) is bounded if and only if αi(G) is bounded for at least one i, 2 ≤ i ≤ (diam(G) - 1)/4.