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Yes. See this paper of Negami. The main result is that for any fixed knot (or link) of type $k$, there is a constant $R(k)$ such that every straight line embedding of $K_{R(k)}$ in $\mathbb{R}^3$ contains a knot (or link) of equivalent to $k$.
Yes. See this paper of Negami. The main result is that for any fixed knot (or link) of type $k$, there is a constant $R(k)$ such that every straight line embedding of $K_{R(k)}$ in $\mathbb{R}^3$ contains a knot (or link) of equivalent to $k$.
Yes. See this paper of Negami. The main result is that for any fixed knot (or link) of type $k$, there is a constant $R(k)$ such that every straight line embedding of $K_{R(k)}$ in $\mathbb{R}^3$ contains a knot (or link) equivalent to $k$.
Yes. See this paper of Negami. The main result is that for any fixed knot (or link) of type $k$, there is a constant $R(k)$ such that every straight line embedding of $K_{R(k)}$ in $\mathbb{R}^3$ contains a knot (or link) of equivalent to $k$.
