2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156759In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing. New examples of surface singularities with rational homology disk smoothings are also presented; these include singularities with resolution graph having valency four nodes.61 pages, 28 figuresGeometric TopologyAlgebraic Geometrytext