Characterizing path graphs by forbidden induced subgraphs
  A graph is a path graph if it is the intersection graph of a family of subpaths of a tree. In 1970, Renz asked for a characterizaton of path graphs by forbidden induced subgraphs. Here we answer this question by listing all graphs that are not path graphs and are minimal with this property. 
Benjamin L\'ev\^eque (LGS), Fr\'ed\'eric Maffray (LGS), Myriam   Preissmann (LGS)