The Heawood graph and $K_{3,3}$ have the property that all of their 2-factors are Hamilton circuits. We call such graphs 2-factor hamiltonian. We prove that if G is a k-regular bipartite 2-factor hamiltonian graph then either G is a circuit or k = 3. Furthermore, we construct an infinite family of cubic bipartite 2-factor hamiltonian graphs based on the Heawood graph and $K_{3,3}$ and conjecture that these are the only such graphs.

2-Factor hamiltonian graphs

FUNK, Martin;LABBATE, Domenico;
2003

Abstract

The Heawood graph and $K_{3,3}$ have the property that all of their 2-factors are Hamilton circuits. We call such graphs 2-factor hamiltonian. We prove that if G is a k-regular bipartite 2-factor hamiltonian graph then either G is a circuit or k = 3. Furthermore, we construct an infinite family of cubic bipartite 2-factor hamiltonian graphs based on the Heawood graph and $K_{3,3}$ and conjecture that these are the only such graphs.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11563/417
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