We present and describe the solver OBLX for the Dominating Set problem on graphs. This solver was developed during the PACE challenge 2025 for the Exact track. It first applies several data reduction rules and performs a polynomial time reduction to Max Sat. The resulting Max Sat instance is in turn solved using the EvalMaxSat solver by Florent Avellaneda.

Given a set P of paths over a graph, its edge intersection graph is a graph each of whose vertices corresponds to a path in P and where two vertices are connected if and only if the paths they correspond to share at least one edge. EPT is the class of edge intersection graphs of paths over trees. The complete characterization of EPT graphs by minimal forbidden subgraphs is not yet known. In this paper, we introduce two stretching operations on graphs and show that they preserve the property of being non-EPT graphs. We further investigate how to use these operations to construct minimal non- EPT graphs, allowing us to present one of the main results of this contribution, that is, two new infinite families of minimal non-EPT graphs that have not yet been described in the literature.