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The interlace polynomial of a graph

Arratia, Richard, Bollobás, Béla and Sorkin, Gregory B. (2004) The interlace polynomial of a graph. Journal of Combinatorial Theory, Series B, 92 (2). pp. 199-233. ISSN 0095-8956

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Abstract

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 Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers.

Item Type: Article
Official URL: http://www.elsevier.com/wps/find/journaldescriptio...
Additional Information: © 2004 Elsevier Inc.
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Research centres and groups > Management Science Group
Departments > Management
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 13 Apr 2011 14:22
URL: http://eprints.lse.ac.uk/35487/

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