Decomposition Of Balanced Complete Bipartite Graphs Into Cycles Of Two Different Length

Abstract

  We decomposing the balanced complete bipartite graph  into ’s and ’s. In particular, we find necessary and sufficient conditions for accomplishing this when  for  As a consequence, we show that for nonnegative integers  and  with , there exists a decomposition of the balanced complete bipartite graph  into  copies of  and  copies of  if and only if  except when  is odd and  is even.