# Interlace polynomial: A new graph polynomial

## Abstract

We define a new graph polynomial, the interlace polynomial, for any undirected graph. Also, we show how to count Euler circuits and circuit decompositions for any directed or undirected Eulerian graph, by a straightforward reduction formula. For 2-in, 2-out directed graphs D, any Euler circuit induces an undirected `interlace' graph H, and there is a close relationship between the number of circuit decompositions of D and the interlace polynomial of H. We explore this relationship, and properties of the interlace polynomial in general.

## Publication Title

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

## Recommended Citation

Arratia, R., Bollobas, B., & Sorkin, G.
(2000). Interlace polynomial: A new graph polynomial.* Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*, 237-245.
Retrieved from https://digitalcommons.memphis.edu/facpubs/4956