Computational complexity of covering three-vertex multigraphs

Abstract. A covering projection from a graph G to a graph H is a mapping of the vertices of G to the vertices of H such that, for every vertex v of G, the neighborhood of v is mapped bijectively to the neighborhood of its image. Moreover, if G and H are multigraphs, then this local bijection has to preserve multiplicities of the neighbors as well. The notion of covering projection stems from topology, but has found applications in areas such as the theory of local computation and construction of highly symmetric graphs. It provides a restrictive variant of the constraint satisfaction problem with additional symmetry constraints on the behavior of the homomorphisms of the structures involved. We investigate the computational complexity of the problem of deciding the existence of a covering projection from an input graph G to a fixed target graph H. Among other partial results this problem has been shown to be NP-hard for simple regular graphs H of valency greater than 2, and a full cha...

• Type: Journal
• Year: 2016
• Where: TCS
• Authors: Jan Kratochvíl, Jan Arne Telle, Marek Tesar
• Keywords: TCS 2016, Theoretical Computer Science