Related papers: Chromatic Derivatives, Chromatic Expansions and As…
Chromatic derivatives and series expansions of bandlimited functions have recently been introduced in signal processing and they have been shown to be useful in practical applications. We extend the notion of chromatic derivative using…
We study differential operators associated with families of polynomials orthonormal with respect to certain measures. These operators, when applied to the Fourier transforms of such measures, produce basis functions for expansions of…
The chromatic polynomials are studied by several authors and have important applications in different frameworks, specially, in graph theory and enumerative combinatorics. The aim of this work is to establish some properties of the…
Using the definition of colouring of $2$-edge-coloured graphs derived from $2$-edge-coloured graph homomorphism, we extend the definition of chromatic polynomial to $2$-edge-coloured graphs. We find closed forms for the first three…
This paper describes how many known graph polynomials arise from the coefficients of chromatic symmetric function expansions in different bases, and studies a new polynomial arising by expanding over a basis given by chromatic symmetric…
Graph polynomials are polynomials assigned to graphs. Interestingly, they also arise in many areas outside graph theory as well. Many properties of graph polynomials have been widely studied. In this paper, we survey some results on the…
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…
We consider s-chromatic polynomials of simplicial complexes, higher dimensional analogues of chromatic polynomials for graphs.
We prove a general inclusion-exclusion relation for the extended chromatic symmetric function of a weighted graph, which specializes to (extended) $k$-deletion, and we give two methods to obtain numerous new bases from weighted graphs for…
In this article we describe a new inductive approach to compute the chromatic polynomial of simple graphs and the characteristic polynomial of central hyperplane arrangements.
We introduce the characteristic numbers and the chromatic polynomial of a tensor. Our approach generalizes and unifies the chromatic polynomial of a graph and of a matroid, characteristic numbers of quadrics in Schubert calculus, Betti…
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very…
For a simple graph $G$, let $\chi(G,x)$ denote the chromatic polynomial of $G$. This manuscript introduces some polynomials which are related to chromatic polynomial and their relations.
We establish closed-form expansions for the number of colorings of a path or cycle on n vertices with colors from 1,...,x such that adjacent vertices are colored differently or with colors from y+1,...x.
The differential expansion is one of the key structures reflecting group theory properties of colored knot polynomials, which also becomes an important tool for evaluation of non-trivial Racah matrices. This makes highly desirable its…
The orbital bivariate chromatic polynomial, introduced in this article, counts the number of ways to color the vertices of a graph with $\lambda$ colors such that adjacent vertices either receive distinct colors from a set of $\lambda$…
One aim of this paper is to develop some aspects of the theory of monoidal derivators. The passages from categories and model categories to derivators both respect monoidal objects and hence give rise to natural examples. We also introduce…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures: the first coproduct is given by partitions of vertices into two parts, the second one by a…
We establish a set of recursion relations for the coefficients in the chromatic polynomial of a graph or a hypergraph. As an application we provide a generalization of Whitney's broken cycle theorem for hypergraphs, as well as deriving an…