ORTHOGONAL DOUBLE COVERS OF COMPLETE BIPARTITE GRAPHS BY PATHS AND CYCLES
An orthogonal double cover (ODC) of a graph H is a collection of subgraphs of H such that (i) every edge of H is contained in exactly two members of and (ii) for any two different members and in is 1 if u and v are adjacent in H and is 0 otherwise. It is proved that the complete bipartite graph for p prime, has an ODC by a path of length p. It is also shown that has an ODC by a cycle of length 10 and by the disjoint union of two cycles of lengths 6 and 4.
graph decomposition, orthogonal double cover, symmetric starter, suborthogonal double cover.