Combinatorial properties of convex cones in $ \mathbf R<sup>n</sup> $

Authors

  • Mircea Balaj

DOI:

https://doi.org/10.1285/i15900932v19n1p25

Keywords:

Acute convex cone, Convex hull, Intersection graph, Ramsey number

Abstract

In this paper we obtain sets of conditions under which the convex hull of a family of convex copies is an acute cone. Some intersectional results for families of convex sets there are also given. Finally, using two combinatorial results concerning families of convex cones, a lower bound for the Ramsey numbers $R_{2n}(m,3n)$ is established.

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Published

01-01-1999

Issue

Volume 19, Issue 1 (1999)

Section

Articoli

License

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http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode