Non-Hamiltonian 3–Regular Graphs with Arbitrary Girth
نویسنده
چکیده
It is well known that 3–regular 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.
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