Alternating knot diagrams, Euler circuits and the interlace polynomial (Q1840823)

The authors give a simple combinatorial proof of the known fact that if \(K\) is a reduced alternating link diagram with \(n\geq 2\) crossings, then \(\text{det }K\geq n\); this implies that alternating links are nontrivial. Their argument uses the matrix-tree theorem, the BEST theorem, and an elementary extremal property of the interlace polynomial.