Boundary graph classes for some maximum induced subgraph problems

Authors:
Dmitriy S. Malyshev
Affiliations:
National Research University Higher School of Economics, Nizhny Novgorod, Russia 603155 and 603093 and Department of Mathematical Logic and Higher Algebra, National Research University of Nizhny N ...
Venue:
Journal of Combinatorial Optimization
Year:
2014

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Abstract

The notion of a boundary graph class was recently introduced for a classification of hereditary graph classes according to the complexity of a considered problem. Two concrete graph classes are known to be boundary for several graph problems. We formulate a criterion to determine whether these classes are boundary for a given graph problem or not. We also demonstrate that the classes are simultaneously boundary for some continuous set of graph problems and they are not simultaneously boundary for another set of the same cardinality. Both families of problems are constituted by variants of the maximum induced subgraph problem.