Alternating Knot Diagrams, Euler Circuits and the Interlace Polynomial

Authors

P. N. Balister, University of MemphisFollow
B. Bollobás, University of MemphisFollow
O. M. Riordan, Trinity College Cambridge
A. D. Scott, University College London

Abstract

We show that two classical theorems in graph theory and a simple result concerning the interlace polynomial imply that if K is a reduced alternating link diagram with n ≥ 2 crossings, then the determinant of K is at least n. This gives a particularly simple proof of the fact that reduced alternating links are nontrivial. © 2001 Academic Press.

Publication Title

European Journal of Combinatorics

Recommended Citation

Balister, P., Bollobás, B., Riordan, O., & Scott, A. (2001). Alternating Knot Diagrams, Euler Circuits and the Interlace Polynomial. European Journal of Combinatorics, 22 (1), 1-4. https://doi.org/10.1006/eujc.2000.0434