论文标题
$（n，k，t）$的证明 - 猜想
A Proof of the $(n,k,t)$-Conjectures
论文作者
论文摘要
\ emph {$（n，k，t）$ - graph}是$ n $顶点上的图形，其中每组$ k $顶点都包含$ t $顶点的集团。根据图表的补充，Turán的定理指出，独特的最低$ $（N，K，2）$ - 图是一个公平的分离集团。我们证明，最低$（N，K，T）$ - 图始终是任何$ t $（尽管\允许绝对示例的允许breaws notientions of totrimale示例）始终是不相交的工会，从而概括了Turán的定理，并确认了Hoffman等人的两个猜想。
An \emph{$(n,k,t)$-graph} is a graph on $n$ vertices in which every set of $k$ vertices contains a clique on $t$ vertices. Turán's Theorem, rephrased in terms of graph complements, states that the unique minimum $(n,k,2)$-graph is an equitable disjoint union of cliques. We prove that minimum $(n,k,t)$-graphs are always disjoint unions of cliques for any $t$ (despite \allowbreak nonuniqueness of extremal examples), thereby generalizing Turán's Theorem and confirming two conjectures of Hoffman et al.
