منابع مشابه
An update on the Hirsch conjecture: Fifty-two years later
The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n− d. That is to say, we can go from any vertex to any other vertex using at most n− d edges. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite s...
متن کاملAn Approach to Hirsch Conjecture
W.M. Hirsch formulated a beautiful conjecture on amaximum of diameters of convex polyhedrawith both fixed dimension and number of facets. This is still unsolved for about 50 years. Here, I suggest a new method of argument from the viewpoint of deformation of polytope. As a candidate of the clue to the complete-proof, there’s some conjectures which are all sufficient for the original problem.
متن کاملAn Approach to the Hirsch Conjecture
W. M. Hirsch proposed a beautiful conjecture on diameters of convex polyhedra, which is still unsolved for about 50 years. I suggest a new method of argument from the viewpoint of deformation and moduli of polytopes. As a consequence, for example, if there are at least 3 disjoint geodisics for all Dantzig figures, as in the 3 dimensional case, the conjecture follows.
متن کاملWho Solved the Hirsch Conjecture?
However, empirical experience with thousands of practical problems indicates that the number of iterations is usually close to the number of basic variables in the final set which were not present in the initial set. For an m-equation problem with m different variables in the final basic set, the number of iterations may run anywhere from m as a minimum, to 2m and rarely to 3m. The number is us...
متن کاملA counterexample to the Hirsch conjecture
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 wit...
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ژورنال
عنوان ژورنال: Jahresbericht der Deutschen Mathematiker-Vereinigung
سال: 2010
ISSN: 0012-0456,1869-7135
DOI: 10.1365/s13291-010-0001-8