<p>The current paper analyzes minimum cost spanning tree problems having irreducible costs while incorporating revenues. We prove that, in this context, the core of the associated cost-revenues game (the <i>r</i>-core) is non-empty. In particular, we find an stable allocation in the <i>r</i>-core, based on the CEL bankruptcy rule, that ensures fairness by distributing revenues only among agents that belong to every effective coalition. Therefore, our findings contribute to the literature by identifying structural conditions that guarantee stability in minimum cost spanning tree problems with revenues, overcoming previous results which showed that the <i>r</i>-core could be empty.</p>