关于三角形生成的赋权图的锥
On the cone of weighted graphs generated by triangles
摘要：
出于涉及三角形分解的图的问题，我们检查锥$τ_n$的加权图上的三角形生成的$n$顶点的刻面结构。我们的研究结果包括枚举小$n$的方面，建设生产方面的$τ_{n+1}$从方面的$τ_n$，和算术条件的条目的法向量。我们还指出，一个副本$τ_n$本质上出现通过周长不等式在一个顶点的度量多面体。
英文摘要：
Motivated by problems involving triangle-decompositions 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.
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