Cycle Systems

Abstract

In this dissertation the author has found the necessary and sufficient conditions for obtaining a 6-cycle system of the Cartesian product of two complete graphs covering 2-paths in the corresponding bipartite graph. She has found the maximum fair 6-cycle system as well as 6-cycle system of the Cartesian product of two complete graphs. As a part of this dissertation, the author has also found the necessary and sufficient conditions required to obtain a 4-cycle system of complete graph on n vertices with a nearly 2-regular leave. Finally the author has worked on the problem of finding a 4-cycle system of the line graph of a complete multipartite graph.