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- W2963983887 abstract "The contact graph of a packing of translates of a convex body in Euclidean d-space Ed is the simple graph whose vertices are the members of the packing, and whose two vertices are connected by an edge if the two members touch each other. A packing of translates of a convex body is called totally separable, if any two members can be separated by a hyperplane in Ed disjoint from the interior of every packing element. We give upper bounds on the maximum degree (called separable Hadwiger number) and the maximum number of edges (called separable contact number) of the contact graph of a totally separable packing of n translates of an arbitrary smooth convex body in Ed with d=2,3,4. In the proofs, linear algebraic and convexity methods are combined with volumetric and packing density estimates based on the underlying isoperimetric (resp., reverse isoperimetric) inequality." @default.
- W2963983887 created "2019-07-30" @default.
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- W2963983887 date "2018-10-01" @default.
- W2963983887 modified "2023-09-27" @default.
- W2963983887 title "On contact graphs of totally separable packings in low dimensions" @default.
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- W2963983887 doi "https://doi.org/10.1016/j.aam.2018.08.003" @default.
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