| A graphic degree sequence, pi, is said to be potentially P-graphic if there exists some graph G realizing pi with property P. We investigate when the property P is subgraph containment. For a fixed graph H, we define sigma(H, n) to be the minimum even integer such that any n-term graphic sequence with sum at least sigma( H, n) has some realization containing H as a subgraph. Using the degree stripping method, we determine sigma(H, n) for two classes of graphs: Fk, which denotes k triangles intersecting in a point, and complete, balanced bipartite graphs. Additionally, we give a lower bound on sigma(H, n) which is sharp for many choices of H. We conjecture that this correctly gives sigma(H, n) for an arbitrarily chosen H. |
