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Prism-Hamiltonicity of triangulations. (English) Zbl 1136.05013

Summary: The prism over a graph \(G\) is the Cartesian product \(G \square K_{2}\) of \(G\) with the complete graph \(K_{2}\). If the prism over \(G\) is Hamiltonian, we say that \(G\) is prism-Hamiltonian. We prove that triangulations of the plane, projective plane, torus, and Klein bottle are prism-Hamiltonian. We additionally show that every 4-connected triangulation of a surface with sufficiently large representativity is prism-hamiltonian, and that every 3-connected planar bipartite graph is prism-Hamiltonian.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C45 Eulerian and Hamiltonian graphs
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