E186 - Institut für Computergraphik und Algorithmen
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Date (published):
2012
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Number of Pages:
61
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Keywords:
hamilton; graph; hamilton-Kreis
de
hamiltonian; uniquely hamiltonian; graph
en
Abstract:
In 1998, J.A. Bondy and B. Jackson conjectured that every simple uniquely hamiltonian planar graph has at least two vertices of degree two. We shall start by providing an overview on many popular results on the number of hamiltonian cycles in a graph. Furthermore we will review the construcion of a uniquely hamiltonian graph of minimum degree four, made by Fleischner. Finally we try to apply similar techniques to obtain a counterexample to the conjecture made by Bondy and Jackson.
