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On contact graphs of totally separable bodies

Banff International Research Station for Mathematical Innovation and Discovery

Contact graphs have emerged as an important tool in the study of translative packings of convex bodies. The contact graph of a translative packing (that is, non-overlapping translates) of a convex body in Euclidean $d$-space is the (simple) graph whose vertices correspond to the packing elements with two vertices joined by an edge if and only if the two corresponding packing elements touch each other. The contact number of a finite translative packing of a convex body is the number of edges in the contact graph of the packing, while the Hadwiger number of a convex body is the maximum vertex degree over all such contact graphs. A translative packing of a convex body in Euclidean d-space is called a totally separable packing if any two packing elements can be separated by a hyperplane disjoint from the interior of every packing element. In this talk, we investigate the Hadwiger and contact numbers of totally separable translative packings of convex bodies.

Mathematics; Functional analysis; Convex and discrete geometry

video/mp4

Author affiliation: University of Calgary

2018-09-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67251

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/