arXiv subjects
Publications and source records attributed to Benjamin Bergougnoux.
We prove that one can count in polynomial time the number of minimal transversals of $β$-acyclic hypergraphs. In consequence, we can count in polynomial time the number of minimal dominating sets of strongly chordal graphs, continuing the line of research initiated in [M.M. Kanté and T. Uno, Counting Minimal Dominating Sets, TAMC'17].
A forbidden transition graph is a graph defined together with a set of permitted transitions i.e. unordered pair of adjacent edges that one may use consecutively in a walk in the graph. In this paper, we look for the smallest set of transitions needed to be able to go from any vertex of the given graph to any other. We prove that this problem is NP-hard and study approximation algorithms. We develop theoretical tools that help to study this problem.