General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite Graph

Abstract

An orthogonal double cover (ODC) of the complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper, we consider the case where the graph to be covered twice is the complete bipartite graphKmn,mn(for any values ofm,n) and all graphs in the collection are isomorphic to certain spanning subgraphs. Furthermore, the ODCs ofKn,nby certain disjoint stars are constructed.

Orthogonal Double Covers of Complete Bipartite Graphs by Paths and Cycles

“…three results, established in[3], were often used as a tool to construct ODCs (see, e.g.,[4][5][6]). We shall apply them yet another time, to prove Theorem 2.4.Theorem 2.1.…”