Paper title: Enumerating Hamiltonian Cycles in a Planar Graph Using Combinatorial Cycle Bases
DOI: https://doi.org/10.4316/JACSM.201601006
Published in: Issue 1, (Vol. 10) / 2016Download
Publishing date: 2016-04-14
Pages: 36-41
Author(s): MAHARESI Retno
Abstract. Cycle bases belong to a k-connected simple graph used 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.
Keywords: Enumeration, Hamiltonian Cycle, Planar, Cycle Bases, Connected Graph
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