A connected digraph in which the in-degree of any vertex equals its
out-degree is Eulerian, this baseline result is used as the basis of existence
proofs for universal cycles (also known as generalized deBruijn cycles or
U-cycles) of several combinatorial objects. We extend the body of known results
by presenting new results on the existence of universal cycles of monotone,
"augmented onto", and Lipschitz functions in addition to universal cycles of
certain types of lattice paths and random walks.Comment: 21 pages, 4 figure