•P7 - Factorization of complete bipartite multigraphs

Abstract

-factorization of a complete bipartite graph for p an integer was studied by Wang [1]. Further, Beiliang [2] extended the work of Wang [1], and studied the -factorization of complete bipartite multigraphs. For even value of k in -factorization, the spectrum problem is completely solved [1, 2, 3]. However for odd value of k i.e. , , and , the path factorization have been studied by a number of researchers [4, 5, 6, 7]. Again, -factorizations of complete bipartite multigraphs and symmetric complete bipartite multi-digraphs were studied by Wang and Beiliang [8]. In the present paper, we study - factorization of complete bipartite multigraphs and show that the necessary and sufficient conditions for the existence of - factorization of complete bipartite multigraph are:

(1)
(2)
(3)
(4) is an integer.