Journals Information
Universal Journal of Applied Mathematics Vol. 2(1), pp. 72 - 78
DOI: 10.13189/ujam.2014.020111
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Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth
M. Haythorpe *
Flinders University
ABSTRACT
It is well known that 3regular graphs with arbitrarily large girth exist. Three constructions are given that use the former to produce non-Hamiltonian 3-regular graphs without reducing the girth, thereby proving that such graphs with arbitrarily large girth also exist. The resulting graphs can be 1-, 2- or 3-edge-connected depending on the construction chosen. From the constructions arise (naive) upper bounds on the size of the smallest non-Hamiltonian 3-regular graphs with particular girth. Several examples are given of the smallest such graphs for various choices of girth and connectedness.
KEYWORDS
Girth, Cages, Cubic, 3-Regular, Prisons, Hamiltonian, non-Hamiltonian
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] M. Haythorpe , "Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth," Universal Journal of Applied Mathematics, Vol. 2, No. 1, pp. 72 - 78, 2014. DOI: 10.13189/ujam.2014.020111.
(b). APA Format:
M. Haythorpe (2014). Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth. Universal Journal of Applied Mathematics, 2(1), 72 - 78. DOI: 10.13189/ujam.2014.020111.