Boundary properties of graphs for algorithmic graph problems

Korpelainen, Nicholas; Lozin, Vadim V.; Malyshev, Dmitriy S. and Tiskin, Alexander (2011). Boundary properties of graphs for algorithmic graph problems. Theoretical Computer Science, 412(29) pp. 3545–3554.

DOI: https://doi.org/10.1016/j.tcs.2011.03.001

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 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.

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About

• Item ORO ID
• 38889
• Item Type
• Journal Item
• ISSN
• 0304-3975
• Keywords
• computational complexity; hereditary class; Hamiltonian cycle; vertex colorability
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2011 Elsevier B.V.
• Depositing User
• Nicholas Korpelainen