Progress on the Traceability Conjecture for Oriented Graphs (Formula‪)‬

1 Introduction The set of vertices and the set of arcs of a digraph D are denoted by V(D) and A(D), respectively, and the order of D is denoted n(D). A directed cycle (path, walk) in a digraph will simply be called a cycle (path, walk). A digraph is hamiltonian if it contains a cycle that visits every vertex, traceable if it contains a path that visits every vertex, walkable (or unilaterally connected) if it contains a walk that visits every vertex, and strong (or strongly connected) if it has a closed walk that visits every vertex.