## Decidability Questions for Graph k-Coverings (1997)

Citations: | 2 - 0 self |

### BibTeX

@MISC{Demichelis97decidabilityquestions,

author = {François Demichelis and Wieslaw Zielonka},

title = {Decidability Questions for Graph k-Coverings},

year = {1997}

}

### OpenURL

### Abstract

. The notion of k-coverings of graphs, used previously in order to demonstrate some impossibility results for local graph computations, is investigated systematically. It turns out that, unlike the classical graph coverings where a simple method exists to construct them effectively for a given graph, k-coverings do not admit any such algorithm --- the problem if a graph admits a nontrivial k-covering appears to be undecidable. 1 Introduction Our aim is to examine a special family of graph maps introduced in [12] and called k-coverings. By a graph we shall always mean an undirected simple graph G with a set V (G) of vertices and a set E(G) of edges, each edge e 2 E(G) being a pair e = fv; wg of two distinct vertices. Then a graph map f : H ! G from a graph H to a graph G is a mapping from V (H) [E(H) into V (G) [ E(G) such that -- f maps vertices (edges) of H to vertices (respectively edges) of G and, -- f preserves the adjacency between vertices and edges: if v 2 V (H) is adjacent...