Boundary properties of graphs for algorithmic graph problems

Authors:
Nicholas Korpelainen;Vadim V. Lozin;Dmitriy S. Malyshev;Alexander Tiskin
Affiliations:
DIMAP and Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK;DIMAP and Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK;Department of Applied Mathematics and Informatics, Higher School of Economics (Nizhny Novgorod branch), Bolshaya Pecherskaya str. 25/12, 603155, Nizhny Novgorod, Russia and Department of Mathemati ...;DIMAP and Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

The notion of a boundary graph property was recently introduced as a relaxation of that of a minimal property and was applied to several problems of both algorithmic and combinatorial nature. In the present paper, we first survey recent results related to this notion and then apply it to two algorithmic graph problems: Hamiltonian cycle and vertexk-colorability. In particular, we discover the first two boundary classes for the Hamiltonian cycle problem and prove that for any k3 there is a continuum of boundary classes for vertexk-colorability.