Complete positivity and distance-avoiding sets

Title

Complete positivity and distance-avoiding sets

 Author

DeCorte, Evan (McGill University)
de Oliveira Filho, F.M. (TU Delft Discrete Mathematics and Optimization)
Vallentin, Frank (Universität zu Köln)

Date

2020

 Abstract

We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequence of this characterization, it is possible to reprove and improve many results concerning distance-avoiding sets on the sphere and in Euclidean space.


 Subject

Chromatic number of Euclidean space
Copositive programming
Hadwiger-Nelson problem
Harmonic analysis
Semidefinite programming

 To reference this document use:

http://resolver.tudelft.nl/uuid:145db990-90bc-4519-8f5c-15f31050f99f

 DOI

https://doi.org/10.1007/s10107-020-01562-6

 ISSN

0025-5610

 Source

Mathematical Programming, 191 (2), 487-558

 Part of collection

Institutional Repository

 Document type

journal article

 Rights

© 2020 Evan DeCorte, F.M. de Oliveira Filho, Frank Vallentin
Files
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