论文标题
图形的均匀盖
Homotopy Covers of Graphs
论文作者
论文摘要
我们开发了$ \ times $ - homotopicy，基本群体和覆盖适用于非简单图的空间的理论，将现有结果推广到简单图。我们证明，来自有限图的$ \ times $ - 启动可以分解为一次动作，最多一次调整一个顶点，从而概括了\ cite {cs1}的蜘蛛引理。我们定义了覆盖地图的概念，并开发了通用覆盖物和甲板转换的理论，将\ cites {tardifwroncha，atssushita}推广到非简单图形。我们检查了反射图的情况，其中每个顶点至少具有一个循环。我们还证明，这些涵盖地图的同质副本满足了任意图同态同构的同质提升属性，从而概括了\ cites {Matsushita，tardifwroncha}的路径提升结果。
We develop a theory of $\times$-homotopy, fundamental groupoids and covering spaces that apply to non-simple graphs, generalizing existing results for simple graphs. We prove that $\times$-homotopies from finite graphs can be decomposed into moves which adjust at most one vertex at a time, generalizing the spider lemma of \cite{CS1}. We define a notion of homotopy covering map and develop a theory of universal covers and deck transformations, generalizing \cites{TardifWroncha, Matsushita} to non-simple graphs. We examine the case of reflexive graphs, where each vertex has at least one loop. We also prove that these homotopy covering maps satisfy a homotopy lifting property for arbitrary graph homomorphisms, generalizing path lifting results of \cites{Matsushita, TardifWroncha}.
