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On the number of hamiltonian cycles in a maximal planar graph
Author(s) -
Hakimi S. L.,
Schmeichel E. F.,
Thomassen C.
Publication year - 1979
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190030407
Subject(s) - mathematics , combinatorics , planar graph , wheel graph , hamiltonian path , quartic graph , planar , hamiltonian (control theory) , graph , hamiltonian path problem , vertex (graph theory) , graph power , discrete mathematics , outerplanar graph , line graph , voltage graph , computer science , mathematical optimization , computer graphics (images)
We consider the problem of the minimum number of Hamiltonian cycles that could be present in a Hamiltonian maximal planar graph on p vertices. In particular, we construct a p ‐vertex maximal planar graph containing exactly four Hamiltonian cycles for every p ≥ 12. We also prove that every 4‐connected maximal planar graph on p vertices contains at least p /(log 2 p ) Hamiltonian cycles.