On the cone of weighted graphs generated by triangles

Date

2019

Authors

del Valle, Coen
Dukes, Peter J.
Garaschuk, Kseniya

Journal Title

Journal ISSN

Volume Title

Publisher

arXiv

Abstract

Motivated by problems involving triangle-decompositions of graphs, we examine the facet structure of the cone τn of weighted graphs on n vertices generated by triangles. Our results include enumeration of facets for small n, a construction producing facets of τn+1 from facets of τn, and an arithmetic condition on entries of the normal vectors. We also point out that a copy of τn essentially appears via the perimeter inequalities at one vertex of the metric polytope.

Description

Keywords

Citation

Del Valle, C., Dukes, P. J., & Garaschuk, K. (2019). On the cone of weighted graphs generated by triangles. arXiv. https://arxiv.org/abs/1608.06017