On interval edge colorings of image)-biregular bipartite graphs

A bipartite graph G is called image-biregular if all vertices in one part of G have degree image and all vertices in the other part have degree image. An edge coloring of a graph G with colors image is called an interval t-coloring if the colors received by the edges incident with each vertex of G are distinct and form an interval of integers and at least one edge of G is colored i, for image. We show that the problem to determine whether an image-biregular bipartite graph G has an interval t-coloring is image-complete in the case when image, image and image. It is known that if an image-biregular bipartite graph G on m vertices has an interval t-coloring then image, where image is the greatest common divisor of image and image. We prove that if an image-biregular bipartite graph has image vertices then the upper bound can be improved to image.