Name
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. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1016/j.jctb.2004.03.003 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
circle graph,tutte polynomial,basic graph property,. pairing,kauffman bracket,euler circuit,circuit partition,interlace graph,interlace graph polynomial,matrix-tree theorem,pairing,martin polynomial,best theorem,interlace polynomial,various special graph,circuit partition polynomial,isotropic system,extremal.,extremal,graph polynomial,satisfiability | Discrete mathematics,Combinatorics,Stable polynomial,Kauffman polynomial,Tutte polynomial,Bracket polynomial,Reciprocal polynomial,Monic polynomial,Matrix polynomial,Chromatic polynomial,Mathematics | Journal |
Volume | Issue | ISSN |
92 | 2 | Journal of Combinatorial Theory, Series B |
Citations | PageRank | References |
47 | 2.21 | 19 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Richard Arratia | 1 | 182 | 21.00 |
| Béla Bollobás | 2 | 2696 | 474.16 |
| Gregory B. Sorkin | 3 | 597 | 89.64 |