论文标题
图形几乎没有边缘的对称边缘多面体的方面
Facets of Symmetric Edge Polytopes for Graphs with Few Edges
论文作者
论文摘要
对称边缘多面体，也称为邻接多型，是由简单无向图确定的晶格多面体。我们介绍了整数数组\（\ mathrm {maxf}（n，m）\）给出了具有\（n \）顶点的连接图的对称边缘层的最大尺寸，并且\（m \）edges，\（m \）edge，以及通讯序列\ \（\ m m ianfm {\ mathrm {minf}（minf}（n min min minim minim minim minim minim minim minim minim minim minim y minim minim for）。我们建立了在几类稀疏图中获得的方面数量的公式，并为识别这些类别中的方面最大化图提供了部分进展。这些公式本质上是组合的，导致了关于由二项式系数产物总和定义的整数序列的独立有趣的观察结果和猜想。
Symmetric edge polytopes, also called adjacency polytopes, are lattice polytopes determined by simple undirected graphs. We introduce the integer array \(\mathrm{maxf}(n,m)\) giving the maximum number of facets of a symmetric edge polytope for a connected graph having \(n\) vertices and \(m\) edges, and the corresponding sequence \(\mathrm{minf}(n,m)\) of minimal values. We establish formulas for the number of facets obtained in several classes of sparse graphs and provide partial progress toward conjectures that identify facet-maximizing graphs in these classes. These formulas are combinatorial in nature and lead to independently interesting observations and conjectures regarding integer sequences defined by sums of products of binomial coefficients.
