GRAPHS WITH DISJOINT LINKS IN EVERY SPATIAL EMBEDDING-Reference-Cited by-同舟云学术

GRAPHS WITH DISJOINT LINKS IN EVERY SPATIAL EMBEDDING

Published:2004-09 Issue:06 Volume:13 Page:737-748
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

CHAN STEPHAN¹,DOCHTERMANN ANTON²,FOISY JOEL³,HESPEN JENNIFER⁴,KUNZ EMAN⁵,LALONDE TRENT⁶,LONEY QUINCY⁷,SHARROW KATHERINE⁸,THOMAS NATHAN⁹

Affiliation:

1. University of Chicago, Chicago, IL 60637, USA

2. Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA

3. Mathematics Department, SUNY Potsdam, Potsdam, NY 13676, USA

4. Department of Statistics, University of Tennessee at Knoxville, Knoxville, TN 37796, USA

5. Mathematics Department, University of Purdue, West Lafayette, IN 47907-2067, USA

6. Department of Mathematics, Univ. of Wisconsin, Madison, WI 53706-1388, USA

7. Mathematics Department, University of Iowa, Iowa City, IA 52242, USA

8. Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA

9. Colorado School of Mines, Golden, CO 80401, USA

Abstract

We exhibit a graph, G12, that in every spatial embedding has a pair of non-splittable 2 component links sharing no vertices or edges. Surprisingly, G12 does not contain two disjoint copies of graphs known to have non-splittable links in every embedding. We exhibit other graphs with this property that cannot be obtained from G12 by a finite sequence of Δ-Y and/or Y-Δ exchanges. We prove that G12 is minor minimal in the sense that every minor of it has a spatial embedding that does not contain a pair of non-splittable 2 component links sharing no vertices or edges.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216504003421

Reference4 articles.

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3. R. Motwani, A. Raghunathan and H. Saran, 29th Annual Symposium on Foundations of Computer Science (IEEE, 1988) pp. 398–409.

4. Linkless embeddings of graphs in 3-space

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