# Simon Špacapan: Prism-hamiltonicity of planar graphs

Date of publication: 14. 11. 2020

Discrete mathematics seminar

Torek, 17. 11. 2020, ob 10:15, na daljavo

**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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