Abstract
An orthogonal double cover (ODC) of a graph H is a collection G = {G sub( v) : v [isin] V(H)} of subgraphs of H such that (i) every edge of H is contained in exactly two members of G, and (ii) for any two different members G sub( u) and G sub( v) in G, |E(G sub( u)) E(G sub( v))| is 1 if u and v are adjacent in H and is 0 otherwise. It is proved that the complete bipartite graph K sub( p, p,) for p prime, has an ODC by a path of length p. It is also shown that K sub( 10, 10) has an ODC by a cycle of length 10 and by the disjoint union of two cycles of lengths 6 and 4.