REGULAR PROJECTIONS OF GRAPHS WITH AT MOST THREE DOUBLE POINTS-Reference-Cited by-同舟云学术

REGULAR PROJECTIONS OF GRAPHS WITH AT MOST THREE DOUBLE POINTS

Published:2010-07 Issue:07 Volume:19 Page:917-933
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

HUH YOUNGSIK¹,NIKKUNI RYO²

Affiliation:

1. Department of Mathematics, School of Natural Sciences, Hanyang University, Seoul 133-791, Korea

2. Department of Mathematical Sciences, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japan

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216510008261

Reference14 articles.

1. V. I. Arnold, Topology of Real Algebraic Varieties and Related Topics, American Mathematical Society Translation Series 2 173 (American Mathematical Society, Providence, RI, 1996) pp. 17–32.

2. Graph minor theory

3. NEWLY FOUND FORBIDDEN GRAPHS FOR TRIVIALIZABILITY

4. R. Nikkuni, Knot Theory for Scientific Objects, Osaka City University Advanced Mathematical Institute Studies 1 (Osaka Municipal Universities Press, 2007) pp. 111–128.