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

Pages (fromto)  245268 
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/facetstri9.txt
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