TRIANGLE-Y EXCHANGES ON INTRINSIC KNOTTING OF ALMOST COMPLETE AND COMPLETE PARTITE GRAPHS-Reference-Cited by-同舟云学术

TRIANGLE-Y EXCHANGES ON INTRINSIC KNOTTING OF ALMOST COMPLETE AND COMPLETE PARTITE GRAPHS

Published:2012-04 Issue:04 Volume:21 Page:1250034
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

LI YANG¹,QIN JIAHU²,LEI FENGCHUN³,WANG XIANGKE⁴,ZHANG XIHAI⁵

Affiliation:

1. Department of Applied Mathematics, Beijing Technology and Business University, Beijing, 100048, China

2. Research School of Engineering, The Australian National University, Canberra, ACT 2600, Australia

3. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

4. College of Mechatronics and Automation, National University of Defense Technology, Changsha, 410073, China

5. School of Engineering, Northeast Agricultural University, Harbin 150030, China

Abstract

Let G be a 0- or 1-deficient graph which is intrinsically knotted, let J represent any graph obtained from G by a finite sequence of Δ-Y exchanges and/or vertex expansions. We prove that removing any vertex of J, and all edges incident to that vertex, yields an intrinsically linked graph. This result provides more intrinsically knotted graphs which satisfy the conjecture mentioned in Adams' The Knot Book that removing any vertex from an intrinsically knotted graph yields an intrinsically linked graph.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021821651100990X

Reference12 articles.

1. SOME RESULTS ON INTRINSICALLY KNOTTED GRAPHS

2. Knots and links in spatial graphs

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1. Deleting an edge of a 3-cycle in an intrinsically knotted graph gives an intrinsically linked graph;Journal of Knot Theory and Its Ramifications;2014-12