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+1from 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.
Original language | English |
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Pages (from-to) | 245-268 |
Number of pages | 24 |
Journal | Journal of Combinatorial Mathematics and Combinatorial Computing |
Volume | 116 |
Publication status | Published - 1 Feb 2021 |
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On the cone of weighted graphs generated by triangles (dataset)
Del Valle, C. (Creator), University of Victoria, 2022
https://www.math.uvic.ca/~dukes/facets-tri9.txt
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