Bi-cycle extendable through a given set in balanced bipartite graphs Original Research Article

Let image be a balanced bipartite graph of order image. The path-cover number image of a graph image is the minimum number of vertex-disjoint paths that use up all the vertices of image. image is called a balanced set of image if image. In this paper, we will give some sufficient conditions for a balanced bipartite graph image satisfying that for every balanced set image, there is a bi-cycle of every length from image up to image through image.