相关论文: Computing the Tutte polynomial in vertex-exponenti…

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…

We give a general fixed parameter tractable algorithm to compute quantum invariants of links presented by diagrams, whose complexity is singly exponential in the carving-width (or the tree-width) of the diagram. In particular, we get a…

The Tutte polynomial is a powerfull analytic tool to study the structure of planar graphs. In this paper, we establish some relations between the number of clusters per bond for planar graph and its dual : these relations bring into play…

The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…

Motivated by the problem of enumerating all tree decompositions of a graph, we consider in this article the problem of listing all the minimal chordal completions of a graph. In \cite{carmeli2020} (\textsc{Pods 2017}) Carmeli \emph{et al.}…

The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving…

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…

A poly-log time method to compute the truncated theta function, its derivatives, and integrals is presented. The method is elementary, rigorous, explicit, and suited for computer implementation. We repeatedly apply the Poisson summation…

In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach…

We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation -- the…

The tensor product $(G_1,G_2)$ of a graph $G_1$ and a pointed graph $G_2$ (containing one distinguished edge) is obtained by identifying each edge of $G_1$ with the distinguished edge of a separate copy of $G_2$, and then removing the…

We introduce the notion of matrices graph, defining continued fraction algorithms where the past and the future are almost independent. We provide an algorithm to convert more general algorithms into matrices graphs. We present an algorithm…

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…

DP-coloring is a generalization of list coloring that was introduced in 2015 by Dvo\v{r}\'{a}k and Postle. The chromatic polynomial of a graph $G$, denoted $P(G,m)$, is equal to the number of proper $m$-colorings of $G$. A well-known tool…

In this article we consider certain well-known polynomials associated with graphs including the independence polynomial and the chromatic polynomial. These polynomials count certain objects in graphs: independent sets in the case of the…

A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph…

We introduce tensor network contraction algorithms for the evaluation of the Jones polynomial of arbitrary knots. The value of the Jones polynomial of a knot maps to the partition function of a $q$-state Potts model defined as a planar…

A generalized vertex join of a graph is obtained by joining an arbitrary multiset of its vertices to a new vertex. We present a low-order polynomial time algorithm for finding the chromatic polynomials of generalized vertex joins of trees,…

We introduce the notions of arithmetic colorings and arithmetic flows over a graph with labelled edges, which generalize the notions of colorings and flows over a graph. We show that the corresponding arithmetic chromatic polynomial and…

The Tutte polynomial of a graph G is a two-variable polynomial T(G;x,y) that encodes many interesting properties of the graph. We study the complexity of the following problem, for rationals x and y: given as input a planar graph G,…