论文标题
简单多面体的边缘连通性
Edge connectivity of simplicial polytopes
论文作者
论文摘要
我们表明，尺寸$ d \ ge 3 $的简单多元化的图形没有少于$ d（d+1）/2 $边缘的非平凡的最小边缘切割，因此该图为$ \ min \ min \ {δ，d（d+1）/2 \} $ - 边缘 - $δ$ DENOTES the最sumimim the Mimumimum the Mimum Mimumimum the Mimum Mimum Mimum Mimum Mimum Mimumimum the Mimum Mimum Mimum Mimum Mimum Mimum Mimum Mimum Mimum Mimum Mimum Miumie。当$ d = 3 $时，这意味着在平面三角剖分中切下的每个最小边缘都是微不足道的。当$ d \ ge 4 $时，我们构建了一个简单的$ d $ - polytope，其图具有非平凡的最小值基数$ d（d+1）/2 $，证明上述结果是最好的。
We show that the graph of a simplicial polytope of dimension $d \ge 3$ has no nontrivial minimum edge cut with fewer than $d(d+1)/2$ edges, hence the graph is $\min\{δ, d(d+1)/2\}$-edge-connected where $δ$ denotes the minimum degree. When $d = 3$, this implies that every minimum edge cut in a plane triangulation is trivial. When $d \ge 4$, we construct a simplicial $d$-polytope whose graph has a nontrivial minimum edge cut of cardinality $d(d+1)/2$, proving that the aforementioned result is best possible.
