SOME RESULTS ON INTRINSICALLY KNOTTED GRAPHS-Reference-Cited by-同舟云学术

SOME RESULTS ON INTRINSICALLY KNOTTED GRAPHS

Published:2007-08 Issue:06 Volume:16 Page:749-760
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

BLAIN PAUL¹,BOWLIN GARRY²,FLEMING THOMAS³,FOISY JOEL⁴,HENDRICKS JACOB⁵,LACOMBE JASON⁶

Affiliation:

1. Department of Mathematics, University of Washington, seattle, WA 98195-4350, USA

2. Department of Mathematics, Binghamton University, Binghamton, NY 13902, USA

3. Deparment of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, USA

4. Department of Mathematics, SUNY Potsdam, Potsdam, NY 13676, USA

5. Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257, USA

6. Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, USA

Abstract

We show that graphs of the form G * K2 are intrinsically knotted if and only if G is nonplanar. This can be extended to show that G * K5m+1 is intrinsically (m + 2)-linked when G is nonplanar. We also apply this result to classify all complete n-partite graphs with respect to intrinsic knotting and show that this family does not produce any new minor-minimal examples. Finally, we categorize all minor-minimal intrinsically knotted graphs on 8 or fewer vertices.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021821650700552X

Reference13 articles.

1. SOME NEW INTRINSICALLY 3-LINKED GRAPHS

2. GRAPHS WITH DISJOINT LINKS IN EVERY SPATIAL EMBEDDING

3. Intrinsically triple linked complete graphs

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