论文标题
多面体连接的简单复合物及其在图理论中的应用
Shellability of Polyhedral Joins of Simplicial Complexes and Its Application to Graph Theory
论文作者
论文摘要
我们研究了$ \ MATHCAL {z}^*_ m（k，l）$ k，m $和subcplex $ l \ subset k $的$ \ mathcal {z}^*_ m（k，l）$。我们在$（k，l）$上提供足够的条件和必要条件。特别是，我们表明，对于某些对$（k，l）$，$ \ MATHCAL {z}^*_ m（k，l）$，无论$ m $是否可撒，$都可以壳。多面体连接可以应用于图理论，作为图形的某些广义版本的独立性复合物，我们在本文中定义了图形。从两个图$ g，h $获得的图形通过将$ h $的一个副本附加到$ g $的每个顶点是此广义词典产品的特殊情况，我们通过应用上述结果来衡量该图的独立性复合体的可壳性。
We investigate the shellability of the polyhedral join $\mathcal{Z}^*_M (K, L)$ of simplicial complexes $K, M$ and a subcomplex $L \subset K$. We give sufficient conditions and necessary conditions on $(K, L)$ for $\mathcal{Z}^*_M (K, L)$ being shellable. In particular, we show that for some pairs $(K, L)$, $\mathcal{Z}^*_M (K, L)$ becomes shellable regardless of whether $M$ is shellable or not. Polyhedral joins can be applied to graph theory as the independence complex of a certain generalized version of lexicographic products of graphs which we define in this paper. The graph obtained from two graphs $G, H$ by attaching one copy of $H$ to each vertex of $G$ is a special case of this generalized lexicographic product and we give a result on the shellability of the independence complex of this graph by applying the above results.
