Variable neighborhood search for extremal graphs. 21. Conjectures and results about the independence number

Authors:
Mustapha Aouchiche;Gunnar Brinkmann;Pierre Hansen
Affiliations:
HEC Montréal, QC, Canada;Dep. of Appl. Math. and Comp. Sci., Ghent University, Ghent, Belgium;GERAD, Montréal, QC, Canada and HEC Montréal, QC, Canada
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

A set of vertices S in a graph G is independent if no neighbor of a vertex of S belongs to S. The independence number @a is the maximum cardinality of an independent set of G. A series of best possible lower and upper bounds on @a and some other common invariants of G are obtained by the system AGX 2, and proved either automatically or by hand. In the present paper, we report on such lower and upper bounds considering, as second invariant, minimum, average and maximum degree, diameter, radius, average distance, spread of eccentricities, chromatic number and matching number.