On the neighbourhood Helly of some graph classes and applications to the enumeration of minimal dominating sets

Abstract

We prove that line graphs and path graphs have bounded neighbourhood Helly. As a consequence, we obtain output-polynomial time algorithms for enumerating the set of minimal dominating sets of line graphs and path graphs. Therefore, there exists an output-polynomial time algorithm that enumerates the set of minimal edge-dominating sets of any graph. © Springer-Verlag Berlin Heidelberg 2012.