Graphic sequences with a realization containing a complete multipartite subgraph

A nonincreasing sequence of nonnegative integers = (d1, d2, ..., dn) is graphic if there is a (simple) graph G of order n having degree sequence . In this case, G is said to realize . For a given graph H, a graphic sequence is potentially H-graphic if there is some realization of containing H as a (weak) subgraph. Let () denote the sum of the terms of . For a graph H and n Z+, (H, n) is defined as the smallest even integer m so that every n-term graphic sequence with () m is potentially H-graphic. Let Kt s denote the complete t partite graph such that each partite set has exactly s vertices. We show that (Kt s, n) = (K(t-2)s + Ks,s, n) and obtain the exact value of (Kj + Ks,s, n) for n sufficiently large. Consequently, we obtain the exact value of (Kt s, n) for n sufficiently large.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Guantao Chen, Michael Ferrara, Ronald J. Gould, John R. Schmitt
• Keywords: DM 2008, Graphic, Nonincreasing Sequence, Nonnegative Integers