NP-hard graph problems and boundary classes of graphs

Authors:
V. E. Alekseev;R. Boliac;D. V. Korobitsyn;V. V. Lozin
Affiliations:
University of Nizhny Novgorod, Gagarina 23, Nizhny Novgorod, 603950, Russia;RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway NJ, 08854-8003, USA;University of Nizhny Novgorod, Gagarina 23, Nizhny Novgorod, 603950, Russia;RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway NJ, 08854-8003, USA
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

Any graph problem, which is NP-hard in general graphs, becomes polynomial-time solvable when restricted to graphs in special classes. When does a difficult problem become easy? To answer this question we study the notion of boundary classes. In the present paper we define this notion in its most general form, describe several approaches to identify boundary classes and apply them to various graph problems.