A counterexample to the Hirsch conjecture
نویسنده
چکیده
The Hirsch Conjecture (1957) stated that the graph of a d-dimensional polytope with n facets cannot have (combinatorial) diameter greater than n−d. That is, any two vertices of the polytope can be connected by a path of at most n− d edges. This paper presents the first counterexample to the conjecture. Our polytope has dimension 43 and 86 facets. It is obtained from a 5-dimensional polytope with 48 facets that violates a certain generalization of the d-step conjecture of Klee and Walkup.
منابع مشابه
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I have been in Seattle only once, in November 2003, when I visited to give a seminar talk at U of W. Victor Klee was already retired (he was 78 at that time), but he came to the department. We had a nice conversation during which he asked "Why don’t you try to disprove the Hirsch Conjecture"? Although I have later found out that he asked the same to many Documenta Mathematica · Extra Volume ISM...
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ورودعنوان ژورنال:
- CoRR
دوره abs/1006.2814 شماره
صفحات -
تاریخ انتشار 2010