The split graph Kr∨Ks on r＋s vertices is denoted by Sr,s A graphic sequence π = （d1, d2, …, dn） is said to be potentially Sr,s-graphic if there is a realization of π containing Sr,s as a subgraph. In this paper...The split graph Kr∨Ks on r＋s vertices is denoted by Sr,s A graphic sequence π = （d1, d2, …, dn） is said to be potentially Sr,s-graphic if there is a realization of π containing Sr,s as a subgraph. In this paper, a simple sufficient condition for π to be potentially Sr,s-graphic is obtained, which extends an analogous condition for π to be potentially Kr＋1-graphic due to Yin and Li （Discrete Math. 301 （2005） 218-227）. As an application of this condition, we further determine the values of δ（Sr,s, n） for n _≥3＋ 3s - 1.展开更多
基金Supported by the National Natural Science Foundation of China(No.11561017)Natural Science Foundation of Guangxi Province(No.2014GXNSFAA118361)Natural Science Foundation of Hainan Province(No.2016CXTD004)
文摘The split graph Kr∨Ks on r＋s vertices is denoted by Sr,s A graphic sequence π = （d1, d2, …, dn） is said to be potentially Sr,s-graphic if there is a realization of π containing Sr,s as a subgraph. In this paper, a simple sufficient condition for π to be potentially Sr,s-graphic is obtained, which extends an analogous condition for π to be potentially Kr＋1-graphic due to Yin and Li （Discrete Math. 301 （2005） 218-227）. As an application of this condition, we further determine the values of δ（Sr,s, n） for n _≥3＋ 3s - 1.
