2 research outputs found
A counterexample to prism-hamiltonicity of 3-connected planar graphs
The prism over a graph is the Cartesian product of with the complete
graph . A graph is hamiltonian if there exists a spanning cycle in
, and is prism-hamiltonian if the prism over is hamiltonian. In
[M.~Rosenfeld, D.~Barnette, Hamiltonian circuits in certain prisms, Discrete
Math. 5 (1973), 389--394] the authors conjectured that every 3-connected planar
graph is prism-hamiltonian. We construct a counterexample to the conjecture
Polyhedra without cubic vertices are prism-hamiltonian
The prism over a graph is the Cartesian product of with the complete
graph on two vertices. A graph is prism-hamiltonian if the prism over
is hamiltonian. We prove that every polyhedral graph (i.e. 3-connected planar
graph) of minimum degree at least four is prism-hamiltonian