On potentially Kr+1 - U-graphical Sequences

摘要

Let K-m - H be the graph obtained from K-m by removing the edges set E(H) of the graph H (H is a subgraph of K-m). We use the symbol Z(4) to denote K-4 - P-2. A sequence S is potentially K-m - H-graphical if it has a realization containing a K-m - H as a subgraph. Let sigma (K-m - H, n) denote the smallest degree sum such that every n-term graphical sequence S with sigma(S) >= sigma(K-m - H, n) is potentially K-m - H-graphical. In this paper, we determine the values of sigma(Kr+1 - U, n) for n >= 5r+18, r+1 >= k > 7, j >= 6 where U is a graph on k vertices and j edges which contains a graph K-3 boolean OR P-3 but not contains a cycle on 4 vertices and not contains Z(4).