A complete solution to the two-table Oberwolfach problems

Even though the Oberwolfach problem has been solved for infinitely many orders, no complete solution is known when the number t of tables is fixed, except for t=1.In this paper we solve all Oberwolfach problems (even those with λ>1) with two table lengths. The fundamental step consists of proving Frucht and Salinasʼ conjecture on the gracefulness of a graph that is a vertex-disjoint union of a cycle and a path.