Skip to main content
Article thumbnail
Location of Repository

The interlace polynomial of a graph

By Richard Arratia, Béla Bollobás and Gregory B. Sorkin

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

Topics: QA Mathematics
Publisher: Elsevier B.V.
Year: 2004
DOI identifier: 10.1016/j.jctb.2004.03.003
OAI identifier: oai:eprints.lse.ac.uk:35487
Provided by: LSE Research Online
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://www.elsevier.com/wps/fi... (external link)
  • http://eprints.lse.ac.uk/35487... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.