The interlace polynomial of graphs at-1

Authors:
P. N. Balister;B. Bollobás;J. Cutler;L. Pebody
Affiliations:
Department of Mathematical Sciences, University of Memphis, Memphis, TN;Department of Mathematical Sciences, University of Memphis, Memphis, TN and Trinity College, Cambridge CB2 1TQ, U.K.;Department of Mathematical Sciences, University of Memphis, Memphis, TN;Department of Mathematical Sciences, University of Memphis, Memphis, TN
Venue:
European Journal of Combinatorics
Year:
2002

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Abstract

In this paper we give art explicit formula for the interlace polynomial at x = - 1 for any graph, and as a result prove a conjecture of Arratia et al. that states that it is always of the form ±2s. We also give a description of the graphs for which s is maximal.