Homotopy covers of graphs
Abstract
We develop a theory of ×-homotopy, fundamental groupoids and covering spaces that applies to non-simple graphs, generalizing existing results for simple graphs. We prove that ×-homotopies from finite graphs can be decomposed into moves that adjust at most one vertex at a time, generalizing the spider lemma of Chih & Scull (2021). We define a notion of homotopy covering map and develop a theory of universal covers and deck transformations, generalizing Matsushita (2017) and Tardif–Wroncha (2019) to non-simple graphs. We examine the case of reflexive graphs (each vertex having 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 Matsushita and Tardif–Wroncha.
Fields of Study & Subjects
Topological and Geometric Data Analysis
Homotopy and Cohomology in Algebraic Topology
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Electronic Journal of Graph Theory and Applications
- Publisher
- The Institute for Research and Community Services (LPPM) ITB
- Volume
- 14
- Issue
- 1
- Pages
- 1–1
- Publication date
- 22 April 2026
- Language
- EN