Work

Computational complexity of covering coloured mixed multigraphs with simple degree partitions

Year: 2026

Type: article

Abstract: The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph H , the H - Cover problem asks if an input graph G allows a graph covering projection onto H . Despite the fact that the quest for characterizing the computational complexity of H - Cover had been started more than 30 years ago, only a handful of general results have been known so far. In this paper, we present a complete characterization of the computational complexity of covering coloured graphs for the case that every equivalence class in the degree partition of the target graph has at most two vertices. We prove this result in a very general form. Following the lines of current development of topological graph theory, we study graphs in the most relaxed sense of the definition. In particular, we consider graphs that are mixed (they may have both directed and undirected edges), may have multiple edges, loops, and semi-edges. We show that a strong P/NP-complete dichotomy holds true in the sense that for each such fixed target graph H , the H - Cover problem is either polynomial-time solvable for arbitrary inputs, or NP-complete even for simple input graphs.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2026.01.019

Authors: Jan Bok, Jiří Fiala, Nikola Jedličková, Jan Kratochvíl, Michaela Seifrtová

Institutions: Centre National de la Recherche Scientifique, Université Clermont Auvergne, Charles University, Clermont Auvergne INP

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Agence Nationale de la Recherche, European Research Council