Rational blow-downs and smoothings of surface singularities
  In 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. 
Andras I. Stipsicz, Zoltan Szabo and Jonathan Wahl