二部图内在纽结的一个充分条件
A sufficient condition for intrinsic knotting of bipartite graphs
摘要：
本文给出了支持一个猜想的证据：一个二部图的每部分至少有五个顶点，|E（G）|\geq 4| V（G）|第17章天生就是一个变态我们证明了猜想的图，恰好有五个或恰好有六个顶点在一个部分。我们还证明了存在常数C_n使得一个二部图的一部分恰好有n个\geq 5个顶点，|E（G）|\geq 4| V（G）|+ C_n是内在纽结的。最后，我们对顶点数不超过10的二部图进行了内在纽结分类。
英文摘要：
We present evidence in support of a conjecture that a bipartite graph with at least five vertices in each part and |E(G)| \geq 4 |V(G)| - 17 is intrinsically knotted. We prove the conjecture for graphs that have exactly five or exactly six vertices in one part. We also show that there is a constant C_n such that a bipartite graph with exactly n \geq 5 vertices in one part and |E(G)| \geq 4 |V(G)| + C_n is intrinsically knotted. Finally, we classify bipartite graphs with ten or fewer vertices with respect to intrinsic knotting.
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