The oriented graph of multi-graftings in the Fuchsian case
  We prove the connectedness and calculate the diameter of the oriented graph of graftings associated to exotic complex projective structures on a compact surface S with a given holonomy representation of Fuchsian type.   The oriented graph of graftings is the graph whose vertices are the equivalence classes of marked CP^1-structures on S with a given fixed holonomy, and there is an oriented edge between two structures if the second is obtained from the first by grafting. 
Gabriel Calsamiglia, Bertrand Deroin, Stefano Francaviglia
math.GT math.DG