Boundary properties of graphs for algorithmic graph problems

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 algorit...

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Bibliographic Details
Published inTheoretical computer science Vol. 412; no. 29; pp. 3545 - 3554
Main Authors Korpelainen, Nicholas, Lozin, Vadim V., Malyshev, Dmitriy S., Tiskin, Alexander
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2011
Subjects
Algorithms
Boundaries
Combinatorial analysis
Computational complexity
Continuums
Graphs
Hamiltonian cycle
Hereditary class
Vertex colorability
Hamiltonian cycle
Computational complexity
Hereditary class
Vertex colorability
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Summary: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 vertex k - colorability. In particular, we discover the first two boundary classes for the Hamiltonian cycle problem and prove that for any k > 3 there is a continuum of boundary classes for vertex k - colorability.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2011.03.001