中文摘要：

-个r-图是-个无环的无向图，其中任何两个顶点之间至多被r条边连接．-个m＋1个顶点的r-完全图，记为K（τ）m＋1，是-个m＋1个顶点的r-图，其中任何两个顶点之间恰好被r条边连接．-个非增的非负整数序列π=（d1，d2，…，dn）称为是r-可图的如果它是某个n个顶点的r-图的度序列,一个r-可图序列π称为是蕴含（强迫）K（τ）m＋1-可图的如果π有-个实现包含K（τ）m＋1作为子图（π的每-个实现包含K（τ）m＋1作为子图）．设σ（K（τ）m＋1，n））（τK（τ）m＋1,n））表示最小的偶整数t，使得每-个r-可图序列π=（d1，d2…，dn）具有∑i=1ndi≥t是蕴含（强迫）K（τ）m＋1-可图的．易见σ（K（τ）m＋1，n）是Erdos等人的-个猜想从1-图到r-图的扩充且τK（τ）m＋1,n）是经典Turan定理从1-图到r-图的扩充．本文给出了蕴含K（τ）m＋1,n）的r-可图序列的两个简单充分条件．此两个条件包含了Yin和Li在[Discrete Math．，2005，301：218—227]中的两个主要结果和当n≥max{m2＋3m＋1-[m2＋m/τ],2m＋1＋[m/τ]}时，σ（K（τ）m＋1，n）之值．此外，我们还确定了当n≥m＋1时，τK（τ）m＋1,n）之值。

英文摘要：

An r-graph is a loopless undirected graph in which no two vertices are joined by more than r edges. An r-complete graph on m ＋ 1 vertices, denoted by K（τ）m＋1, is an r-graph on m ＋ 1 vertices in which each pair of vertices is joined by exactly r edges. A non-increasing sequence π = （d1, d2,..., dn） of nonnegative integers is said to be r-graphic if it is the degree sequence of some r-graph on n vertices. An r-graphic sequence π is said to be potentially （resp. forcibly） K（τ）m＋1-graphic if π has a realization containing K（τ）m＋1 as a subgraph （resp. every realization of π contains K（τ）m＋1 as a subgraph）. Let σ（ K（τ）m＋1, n） （resp. K（τ）m＋1, n）） denote the smallest even integer t n such that each r-graphic sequence π = （d1, d2,..., dn） with ∑i=1ndi≥ t is potentially （resp. forcibly） K（τ）m＋1-graphic. Clearly,σ（ K（τ）m＋1, n） is an extension from 1-graph to r-graph of a conjecture due to Erdos et al and τ（K（τ）m＋1,n） is an extension from 1-graph to r-graph of the classical Turan＇s theorem. In this paper, we give two simple sufficient conditions for an r-graphic sequence to be potentially K（τ）m＋1-graphic, which imply two main results due to Yin and Li （Discrete Math., 2005, 301： 218-227） and the value of σ（K（τ）m＋1, n） for n 〉 max{m2＋3m＋1-[m2＋m/τ],2m＋1＋[m/τ]}. Moreover, we also determine the value of τ（K（τ）m＋1, n） for n 〉 m ＋ 1.