Simon Špacapan: Prism-hamiltonicity of planar graphs

Abstract. The prism over a graph G is the Cartesian product of G with the complete graph on two vertices. A graph G is prism-hamiltonian, if the prism over G is hamiltonian. In this talk we discuss the Barnette-Rosenfeld conjecture which asserts that every 3-connected planar graph is prism-hamiltonian. 

Several partial positive results on the conjecture are presented, and the recent refutation of the general case is described in detail. We conclude the talk with open problems and conjectures.

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