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
Let n 〉 r, let lr --- （dl,d2,-,dn） be a non-increasing sequence of nonnegative integers and let Kr＋l - e be the graph obtained from Kr＋l by deleting one edge. If zr has a realization G containing Kr＋l - e as a s...Let n 〉 r, let lr --- （dl,d2,-,dn） be a non-increasing sequence of nonnegative integers and let Kr＋l - e be the graph obtained from Kr＋l by deleting one edge. If zr has a realization G containing Kr＋l - e as a subgraph, then r is said to be potentially Kr＋l - e-graphic. In this paper, we give a characterization for a sequence π to be potentially Kr＋l - e-graphic.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.
基金Supported by National Natural Science Foundation of China(Nos.11161016 and 10861006)
文摘Let n 〉 r, let lr --- （dl,d2,-,dn） be a non-increasing sequence of nonnegative integers and let Kr＋l - e be the graph obtained from Kr＋l by deleting one edge. If zr has a realization G containing Kr＋l - e as a subgraph, then r is said to be potentially Kr＋l - e-graphic. In this paper, we give a characterization for a sequence π to be potentially Kr＋l - e-graphic.
