NEWLY FOUND FORBIDDEN GRAPHS FOR TRIVIALIZABILITY-Reference-Cited by-同舟云学术

NEWLY FOUND FORBIDDEN GRAPHS FOR TRIVIALIZABILITY

Published:2005-06 Issue:04 Volume:14 Page:523-538
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

NIKKUNI RYO¹,OZAWA MAKOTO²,TANIYAMA KOUKI³,TSUTSUMI YUKIHIRO⁴

Affiliation:

1. Department of Mathematics, Faculty of Education, Kanazawa University, Kakuma-machi, Kanazana, Ishikawa, 920-1192, Japan

2. Natural Science Faculty, Faculty of Letters, Komazawa University, Komazawa 1-23-1, Setagaya-ku, Tokyo, 154-8525, Japan

3. Department of Mathematics, School of Education, Waseda University, Nishi-Waseda 1-6-1, Shinjuku-ku, Tokyo, 169-8050, Japan

4. Department of Mathematics, Faculty of Science and Technology, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama, 223-8522, Japan

Abstract

A planar graph is said to be trivializable if every regular projection of the graph produces a trivial spatial embedding by giving some over/under informations to the double points. Every minor of a trivializable graph is also trivializable, thus the set of forbidden graphs is finite. Seven forbidden graphs for the trivializability were previously known. In this paper, we exhibit nine more forbidden graphs.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216505003932

Reference5 articles.

1. Minimally Knotted Spatial Graphs are Totally Knotted

2. Detecting unknotted graphs in 3-space

3. ON AN EXTENSION OF TRIVIALIZABLE GRAPHS

4. Knotted projections of planar graphs

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On inequalities between unknotting numbers and crossing numbers of spatial embeddings of trivializable graphs and handlebody-knots;Journal of Knot Theory and Its Ramifications;2022-01

2. Unknotting numbers and crossing numbers of spatial embeddings of a planar graph;Journal of Knot Theory and Its Ramifications;2020-12

3. Unknotting numbers for handlebody-knots and Alexander quandle colorings;Journal of Knot Theory and Its Ramifications;2015-12

4. REGULAR PROJECTIONS OF GRAPHS WITH AT MOST THREE DOUBLE POINTS;Journal of Knot Theory and Its Ramifications;2010-07