论文标题
关于多径复合物的同型类型
On the homotopy type of multipath complexes
论文作者
论文摘要
有向图中的多径是路径的不相交联合。有向图$ {\ tt g} $的多径复合体是简单的复合体，其面是$ {\ tt g} $的多径。我们计算了某些图的多径复合体的Euler特性和相关的生成函数，包括及时锦标赛和完整的两部分图。然后，我们计算线性图，多边形，小网格和及时锦标赛的多径络合物的同质类型。我们表明它们都是可签定的或球形的楔形。我们引入了一种新技术，用于将有向图分解为动态区域，这使我们能够简化同型计算。
A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph ${\tt G}$ is the simplicial complex whose faces are the multipaths of ${\tt G}$. We compute the Euler characteristic, and associated generating function, of the multipath complex for some families of graphs, including transitive tournaments and complete bipartite graphs. Then, we compute the homotopy type of multipath complexes of linear graphs, polygons, small grids and transitive tournaments. We show that they are all contractible or wedges of spheres. We introduce a new technique for decomposing directed graphs into dynamical regions, which allows us to simplify the homotopy computations.
