Francisco Santos Leal, Universidad de Cantabria, Diameters of polyhedra and simplicial complexes
SAS 1102The Hirsch conjecture, posed in 1957, stated that the graph of a $d$-dimensional polytope or polyhedron with $n$ facets cannot have diameter greater than $n−d$ . The conjecture itself has been disproved by Klee-Walkup (1967) for unbounded polyhedra and by the speaker (2012) for bounded polytopes; but what we know about the underlying question is…