The Y-triangle move does not preserve intrinsic knottedness
Erica Flapan and Ramin Naimi
Source: Osaka J. Math. Volume 45, Number 1 (2008), 107-111.
Abstract
We answer the question ``Does the Y-triangle move preserve intrinsic knottedness?'' in the negative by giving an example of a graph that is obtained from the intrinsically knotted graph $K_{7}$ by triangle-Y and Y-triangle moves but is not intrinsically knotted.
Primary Subjects: 05C10
Secondary Subjects: 57M25
Full-text: Access granted (open access)
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ojm/1205503559
References
J.H. Conway and C.McA. Gordon: Knots and links in spatial graphs, J. Graph Theory 7 (1983), 445--453.
Mathematical Reviews (MathSciNet):
MR722061
Digital Object Identifier: doi:10.1002/jgt.3190070410
R. Diestel: Graph Theory, Graduate Texts in Mathematics 173, Springer-Verlag, New York, 1997.
Mathematical Reviews (MathSciNet):
MR1448665
Zentralblatt MATH:
0873.05001
R. Motwani, A. Raghunathan and H. Saran: Constructive results from graph minors: Linkless embeddings, 29th Annual Symposium on Foundations of Computer Science, IEEE, 1988, 398\nobreakdash--409.
N. Robertson, P. Seymour and R. Thomas: Sachs' linkless embedding conjecture, J. Combin. Theory Ser. B 64 (1995), 185--227.
Mathematical Reviews (MathSciNet):
MR1339849
Digital Object Identifier: doi:10.1006/jctb.1995.1032
H. Sachs: On spatial representations of finite graphs; in Finite and Infinite sets, Vol. I, II (Eger, 1981), Colloq. Math. Soc. János Bolyai 37, North-Holland, Amsterdam, 1984, 649--662.
Mathematical Reviews (MathSciNet):
MR818267
Zentralblatt MATH:
0568.05026
2008 © Osaka University and Osaka City University, Departments of Mathematics
Osaka Journal of Mathematics
