The interlace polynomial of a graph

@article{Arratia2004TheIP,
  title={The interlace polynomial of a graph},
  author={Richard Arratia and B{\'e}la Bollob{\'a}s and Gregory B. Sorkin},
  journal={J. Comb. Theory, Ser. B},
  year={2004},
  volume={92},
  pages={199-233}
}
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable " interlace polynomial " for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial. It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the… CONTINUE READING
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