An embedding of a graph in $3$-space is linkless if for every two disjoint cycles there exists an embedded ball that contains one of the cycles and is disjoint from the other. We prove that every bipartite linklessly embeddable (simple) graph on $n\ge5$ vertices has at most $3n-10$ edges, unless it is isomorphic to the complete bipartite graph $K_{3,n-3}$.

中文翻译：

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二部无链接可嵌入图的极值函数

如果对于每两个不相交的循环，存在一个包含其中一个循环且与另一个不相交的嵌入球，则在 $3$-空间中嵌入图是无链接的。我们证明 $n\ge5$ 顶点上的每个二部无链接可嵌入（简单）图最多具有 $3n-10$ 边，除非它与完整二部图 $K_{3,n-3}$ 同构。