Related papers: A Tutte polynomial for maps

The U-polynomial, the polychromate and the symmetric function generalization of the Tutte polynomial due to Stanley are known to be equivalent in the sense that the coefficients of any one of them can be obtained as a function of the…

For each graph and each positive integer $n$, we define a chain complex whose graded Euler characteristic is equal to an appropriate $n$-specialization of the dichromatic polynomial. This also gives a categorification of $n$-specializations…

It is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Relying on the results of Bollob\'as and Riordan, we introduce a…

Unlike Whitney's definition of the corank-nullity generating function $T(G;x+1,y+1)$, Tutte's definition of his now eponymous polynomial $T(G;x,y)$ requires a total order on the edges of which the polynomial is a posteriori independent.…

We define a multivariate polynomial that generalizes several interlace polynomials defined by Arratia, Bollobas and Sorkin on the one hand, and Aigner and van der Holst on the other. We follow the route traced by Sokal, who defined a…

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…

The Bollob\'as-Riordan polynomial [Math. Ann. 323, 81 (2002)] is a universal polynomial invariant for ribbon graphs. We find an extension of this polynomial for a particular family of combinatorial objects, called rank 3 weakly-colored…

Thom polynomials are universal cohomological obstructions to the appearance of singularities of given types in differentiable maps. As an application, various invariants of immersions have been expressed in terms of singularities of their…

We establish a relation between the Bollobas-Riordan polynomial of a ribbon graph with the relative Tutte polynomial of a plane graph obtained from the ribbon graph using its projection to the plane in a nontrivial way. Also we give a…

We introduce a new matroid (graph) invariant, the arboricity polynomial. Given a matroid, the arboricity polynomial enumerates the number of covers of the ground set by disjoint independent sets. We establish the polynomiality of the…

In this study, we present two results that relate Tutte polynomials. First, we provide new and complete polynomial invariants for graphs. We note that the number of variables of our polynomials is one. Second, let L_1 and L_2 be two…

We give a new characterization of the Tutte polynomial of graphs. Our characterization is formally close (but inequivalent) to the original definition given by Tutte as the generating function of spanning trees counted according to…

We define a trivariate polynomial combining the NL-coflow and the NL-flow polynomial, which build a dual pair counting acyclic colorings of directed graphs, in the more general setting of regular oriented matroids.

We prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous to the fact that…

We show that the 4-variable generating function of certain orientation related parameters of an ordered oriented matroid is the evaluation at (x + u, y+v) of its Tutte polynomial. This evaluation contains as special cases the counting of…

This is the first one of a series of papers on association of orientations, lattice polytopes, and abelian group arrangements to graphs. The purpose is to interpret the integral and modular tension polynomials of graphs at zero and negative…

We define and study the Tutte polynomial of a hyperplane arrangement. We introduce a method for computing it by solving an enumerative problem in a finite field. For specific arrangements, the computation of Tutte polynomials is then…

In this paper, we introduce the concept of the Tutte polynomials of genus $g$ and discuss some of its properties. We note that the Tutte polynomials of genus one are well-known Tutte polynomials. The Tutte polynomials are matroid…

We prove some variants of the exponential formula and apply them to the multivariate Tutte polynomials (also known as Potts-model partition functions) of graphs. We also prove some further identities for the multivariate Tutte polynomial,…

Inspired by piecewise polynomiality results of double Hurwitz numbers, Ardila and Brugall\'e introduced an enumerative problem which they call double Gromov--Witten invariants of Hirzebruch surfaces. These invariants serve as a…