Enumerating Hamiltonian Cycles in a Planar Graph Using Combinatorial Cycle Bases

Enumerating Hamiltonian Cycles in a Planar Graph Using Combinatorial Cycle Bases


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  • LCC Subject Category:
  • Publisher's keywords: enumeration, Hamiltonian cycle, planar, cycle bases, connected graph
  • Language of fulltext: english
  • Full-text formats available: PDF
  • Time From Submission to Publication:


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sed both for listing and enumerating Hamiltonian cycles contained in a planar graph. Planar cycle bases have a weighted induced graph whose weight values limited to 1. Hence making it was possible used in the Hamiltonian cycle enumeration procedures efficiently. In this paper a Hamiltonian cycle enumeration scheme is obtained through two stages. First, i cycles out of m bases cycles are determined using an appropriate constructed constraint. Secondly, to search all Hamiltonian cycles which are formed by the combination of i bases cycles obtained in the first stage efficiently. This efficiency achieved through a generation a class of objects as the representation of i cycle combinations among m bases cycles. The experiment conducted based on the proposed algorithm successfully generated and enumerated all the Hamiltonian cycles contained in a well-known example of planar graph.

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