Constructing arbitrarily large graphs with a specified number of Hamiltonian cycles

Michael Haythorpe

doi:10.5614/ejgta.2016.4.1.3

Constructing arbitrarily large graphs with a specified number of Hamiltonian cycles

Michael Haythorpe

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 ≥ k ≥ 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.

Original language	English
Pages (from-to)	18-25
Number of pages	8
Journal	Electronic Journal of Graph Theory and Applications
Volume	4
Issue number	1
DOIs	https://doi.org/10.5614/ejgta.2016.4.1.3
Publication status	Published - 2016

Keywords

Broken crown
Graph construction
Hamiltonian cycles

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10.5614/ejgta.2016.4.1.3

Cite this

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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 ≥ k ≥ 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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AB - 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 ≥ k ≥ 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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KW - Graph construction

KW - Hamiltonian cycles

UR - http://www.ejgta.org/index.php/ejgta/article/view/97/pdf_13

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JO - Electronic Journal of Graph Theory and Applications

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ER -

Constructing arbitrarily large graphs with a specified number of Hamiltonian cycles

Abstract

Keywords

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