In a recent paper Arratia, Bollobás and Sorkin discuss a graph polynomial defined recursively, which they call the interlace polynomial q(G, x). They present several interesting results with applications to the Alexander polynomial and state the conjecture that |q(G, -1)| is always a power of 2. In
A Two-Variable Interlace Polynomial
✍ Scribed by Richard Arratia; Béla Bollobás†; Gregory B. Sorkin
- Publisher
- Springer-Verlag
- Year
- 2004
- Tongue
- English
- Weight
- 252 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We show that two classical theorems in graph theory and a simple result concerning the interlace polynomial imply that if K is a reduced alternating link diagram with n ≥ 2 crossings, then the determinant of K is at least n. This gives a particularly simple proof of the fact that reduced alternating
In this paper we give an 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 ±2 s . We also give a description of the graphs for which s is maximal.
The main object of this paper is to construct a two-variable analogue of Jacobi polynomials and to give some properties of these polynomials. We show that these polynomials are orthogonal, then we obtain various recurrence formulas for them. Furthermore, we give some integral representations for the