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Extremal sets of graphs in the problem of demarcation in the family of hereditary closed classes of graphs
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D. S. Malyshev
Published/Copyright:
June 22, 2013
Abstract
In this research we consider minimal hard and boundary classes. These classes are of considerable importance in demarcating the polynomial solvability and the NP-completeness of problems on graphs in the family of hereditary classes. Earlier it was established that there are no minimal hard classes for a certain type of problems on graphs. Here we find a sufficient condition for existence of such classes. With its use we construct new examples of minimal hard classes and boundary classes for some problems on graphs. We provide complete description of the sets of minimal hard and boundary classes for the problems under consideration. Up to now, no such descriptions were known.
Published Online: 2013-06-22
Published in Print: 2012-10
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
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- Statistical problems on random permutations with censored data
- On large deviations of branching processes in a random environment with arbitrary initial number of particles: critical and supercritical cases
- Multitype branching processes evolving in a Markovian environment
- On solutions and algebraic duality of generalised linear discrete time systems
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