Hamiltonicity in polytopes and hyperplane arrangements

Hamiltonian cycles are one of the fundamental concepts in graph theory. On the other hand, many combinatorial generation problems can be translated into questions on Hamiltonian cycles in suitable graphs, so-called flip graphs. In this talk, I will report on recent results and constructions of Hamiltonian cycles in graphs with a geometric origin, such as the graph of the face lattice of a polytope, or the graph of regions of a hyperplane arrangement. This is based on joint work with N. Behrooznia, J. Cardinal, T. McConville, A. Merino, T. Mütze, C. Rieck, and F. Verciani.