Alternating Knot Diagrams, Euler Circuits and the Interlace Polynomial

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.