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REGULAR PROJECTIONS OF GRAPHS WITH AT MOST THREE DOUBLE POINTS.
- Source :
-
Journal of Knot Theory & Its Ramifications . Jul2010, Vol. 19 Issue 7, p917-933. 17p. 27 Diagrams. - Publication Year :
- 2010
-
Abstract
- A generic immersion of a planar graph into the 2-space is said to be knotted if there does not exist a trivial embedding 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. In this paper, we show that if a generic immersion of a planar graph is knotted then the number of double points of the immersion is more than or equal to three. To prove this, we also show that an embedding of a graph obtained from a generic immersion of the graph (does not need to be planar) with at most three double points is totally free if it contains neither a Hopf link nor a trefoil knot. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 19
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 52859589
- Full Text :
- https://doi.org/10.1142/S0218216510008261