The interlace polynomial: a new graph polynomial

  title={The interlace polynomial: a new graph polynomial},
  author={Richard Arratia and B{\'e}la Bollob{\'a}s and Gregory B. Sorkin},
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… CONTINUE READING
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