A graph G , every vertex of which has degree at least three, is randomly 3-axial if for each vertex V of G , any ordered collection of three paths in G of length one with initial vertex V can be cyclically randomly extended to produce three internally disjoint paths which contain all the vertices of G . Randomly 3-axial graphs of order p > k are characterized for p ^ 1 (mod 3) , and are shown t...
