蕴含K4＋P2-可图序列的刻划

对于给定的图H，若存在可图序列π的一个实现包含H作为子图，则称π为蕴含H-可图的．Gould等人考虑了下述极值问题的变形：确定最小的偶整数σ（H，n），使得每个满足σ（π）≥σ（H，n）的n项可图序列π=（d1，d2，…，dn）是蕴含H-可图的，其中σ（π）=∑di．本文刻划了蕴含K4＋P2-可图序列，其中K4＋P2是向致的一个顶点添加两条悬挂边后构成的简单图．这一刻划导出σ（K4＋P2，n）的值．

A Characterization On Potentially K_4 + P_2-graphic Sequences

For a given graph H, a graphic sequence π is potentially H-graphic if there is a realization of π containing H as a subgraph. Gould et al. considered an extremal problem on potentially H-graphic sequences as follows: determine the smallest even integer σ(H,n) such that every n-term positive graphic sequence π=(d_1,d_2,…，d_n) with σ(π)≥σ(H,n) has a realization Gcontaining H as a subgraph, where σ(π) = ∑ d_i. In this paper, we characterize the potentially K_4+P_2-graphic sequences, where K_4 + P_2 is a graph obtained by adding two pendent edges to a vertex on K_4. The characterization implies the value of σ(K_4 + P_2, n).