Hamiltonian cycles through prescribed edges of 4-connected maximal planar graphs |
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Authors: | F Göring |
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Institution: | a Department of Mathematics, Technical University of Chemnitz, Germany b Institute of Mathematics, Technical University of Ilmenau, Germany |
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Abstract: | In 1956, W.T. Tutte proved that every 4-connected planar graph is hamiltonian. Moreover, in 1997, D.P. Sanders extended this to the result that a 4-connected planar graph contains a hamiltonian cycle through any two of its edges. It is shown that Sanders’ result is best possible by constructing 4-connected maximal planar graphs with three edges a large distance apart such that any hamiltonian cycle misses one of them. If the maximal planar graph is 5-connected then such a construction is impossible. |
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Keywords: | Maximal planar graph Hamiltonian cycle Prescribed edges |
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