Graphic sequences with a realization containing a complete multipartite subgraph Original Research Article

A nonincreasing sequence of nonnegative integers image is graphic if there is a (simple) graph image of order image having degree sequence image. In this case, image is said to realize image. For a given graph image, a graphic sequence image is potentially image-graphic if there is some realization of image containing image as a (weak) subgraph. Let image denote the sum of the terms of image. For a graph image and image, image is defined as the smallest even integer image so that every image-term graphic sequence image with image is potentially image-graphic. Let image denote the complete image partite graph such that each partite set has exactly image vertices. We show that image and obtain the exact value of image for image sufficiently large. Consequently, we obtain the exact value of image for image sufficiently large.