Regular Projections of Graphs with at Most Three Double Points

نویسنده

  • YOUNGSIK HUH
چکیده

We investigate some relations between a generic immersion of a graph into the 2-space with small number of double points and the embeddings of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space to the 2-space. Specifically we prove: (1) An embedding of a graph obtained from a generic immersion of the graph with at most three double points is totally free if it contains neither a Hopf link nor a trefoil knot. (2) If a generic immersion of a planar graph does not produce any trivial embedding of the graph, then the number of double points of the immersion is more than or equal to three.

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تاریخ انتشار 2009