On Hadwiger's Covering Conjecture

by T. Bisztriczky

Abstract:

We examine the history of this conjecture which concerns covering a d-dimensional convex by smaller homothetic copies of that body.The problem was formulated in the 1950's and it is still unsolved.There are equivalent formulations of the problem,as well as solutions for specific bodies and for specific dimensions.One solution,for dual cyclic d-polytopes,is due to K.Bezdek and the speaker.

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