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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Michael Haythorpe
School of Computer Science, Engineering and Mathematics, Flinders University, 1284 South Road, Clovelly Park, SA 5042, Australia
Electrical & Electronics Engineering

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Constructing arbitrarily large graphs with a specified number of Hamiltonian cycles Michael Haythorpe
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 1 (2016): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2016.4.1.3

Abstract

A constructive method is provided that outputs a directed graph which is named a broken crown graph, containing $5n-9$ vertices and $k$ Hamiltonian cycles for any choice of integers $n \geq k \geq 4$. The construction is not designed to be minimal in any sense, but rather to ensure that the graphs produced remain non-trivial instances of the Hamiltonian cycle problem even when $k$ is chosen to be much smaller than $n$.
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