On longest circuits in certain non-regular planar graphs
Simple 3-polytopal graphs with edges of only two types and shortness coefficients
Trestles in polyhedral graphs
Note on Petrie and Hamiltonian cycles in cubic polyhedral graphs
In this note we show that deciding the existence of a Hamiltonian cycle in a cubic plane graph is equivalent to the problem of the existence of an associated cubic plane multi-3-gonal graph with a Hamiltonian cycle which takes alternately left and right edges at each successive vertex, i.ei̇t is also a Petrie cycle. The Petrie Hamiltonian cycle in an -vertex plane cubic graph can be recognized by an -algorithm.
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