有一个实现包含Kr +1的可图序列

设K _{r +1}是一个r +1个顶点的完全图. 一个可图序列π =(d₁, d₂,…, d_n)称为是蕴含K _r+1 -可图的, 如果π有一个实现包含 K _{r +1}作为子图. 该文进一步研究了蕴含K _{r+1 -}可图序列的一些新的条件, 证明了这些条件包含文献14,10,11]中的一些主要结果和当n≥5r/2 +1时,σ(K _r+1, n)之值(此值在文献2]中被猜测, 在文献6,7,8,3]中被证实). 此外, 确定了所有满足n≥5, d₅≥4 且不蕴含K₅ -可图序列π=(d₁, d₂,…, d_n)的集合.

Graphic Sequences that Have a Realization Containing an K r+1

Let K _r+1 be the complete graph on r+1 vertices. A graphic sequence π =(d_1,d_2,\cdots ,d_n) is said to be potentially K r+1-graphic if there exists a realization of π containing K _r+1 as a subgraph. In this paper, we further investigate a number of new conditions for π to be potentially K _r+1-graphic, which imply some previous results in 14,10,11] and the values of σ(K _r+1, n) for n ≥ 5r/2 +1, which was conjectured in 2] and was confirmed in 6,7,8,3]. Moreover, we also determine F(4), the set of all graphic sequences π=(d₁, d₂, …, d_n) with n ≥ 5 and d₅ ≥ 4 so that π is not potentially K₅-graphic.