Francisco (Paco) Santos’s paper “A Counterexample to the Hirsch Conjecture” is now out:
Abstract: The Hirsch Conjecture (1957) stated that the graph of a -dimensional polytope with facets cannot have (combinatorial) diameter greater than . That is, that any two vertices of the polytope can be connected to each other by a path of at most edges. This paper presents the first counter-example to the conjecture. Our polytope has dimension 43 and 86 facets. It is obtained from a 5-dimensional polytope with 48 facets which violates a certain generalization of the -step conjecture of Klee and Walkup.
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