论文标题
完整图和完整的两分图的较高匹配的复合物
Higher matching complexes of complete graphs and complete bipartite graphs
论文作者
论文摘要
对于$ r \ geq 1 $，$ r $ - 图$ g $的$ r $，表示为$ m_r（g）$，是一个简单的综合体，其面孔是$ h \ subseteq e（g）$ g $的子集$ h \ subseteq e（g）$ g $的$ g $，因此在诱导的$ g [h] $ $ $ $ r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r。在本文中，我们为$（n-2）$的同型类型提供了一个封闭的表单公式 - $ n $顶点上的完整图的匹配复合物。我们还证明，$（n-1）$ - 完整的双分图的匹配复合物$ k_ {n，n} $是同质的，等于dimension $（n-1）^2-1 $的球体。
For $r\geq 1$, the $r$-matching complex of a graph $G$, denoted $M_r(G)$, is a simplicial complex whose faces are the subsets $H \subseteq E(G)$ of the edge set of $G$ such that the degree of any vertex in the induced subgraph $G[H]$ is at most $r$. In this article, we give a closed form formula for the homotopy type of the $(n-2)$-matching complex of complete graph on $n$ vertices. We also prove that the $(n-1)$-matching complex of complete bipartite graph $K_{n,n}$ is homotopy equivalent to a sphere of dimension $(n-1)^2-1$.
