Related papers: Inductive approach to chromatic and characteristic…

The fractional and circular chromatic numbers are the two most studied non-integral refinements of the chromatic number of a graph. Starting from the definition of a coloring base of a graph, which originated in work related to ergodic…

We provide methods to compute the colored HOMFLY polynomials of knots and links with symmetric representations based on the linear skein theory. By using diagrammatic calculations, several formulae for the colored HOMFLY polynomials are…

The problem "A general characterization of uniqueness polynomial for non-critically injective polynomials" has been remained open since the last two decades. In this paper, we explore this open problem. To this end, we initiate a new…

Let $G=(V,E)$ be a simple graph with $V=\{1,2,\cdots,n\}$ and $\chi(G,x)$ be its chromatic polynomial. For an ordering $\pi=(v_1,v_2,\cdots,v_n)$ of elements of $V$, let $\delta_G(\pi)$ be the number of $i$'s, where $1\le i\le n-1$, with…

We introduce a family of generalized Broughton polynomials and compute the characteristic varieties of complement of a curve arrangement defined by fibers of some generalized Broughton polynomials

We introduce a new one-variable polynomial invariant of graphs, which we call the skew characteristic polynomial. For an oriented simple graph, this is just the characteristic polynomial of its anti-symmetric adjacency matrix. For…

We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description…

The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…

This paper describes an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, this was only…

A \emph{chromatic root} is a root of the chromatic polynomial of a graph. Any chromatic root is an algebraic integer. Much is known about the location of chromatic roots in the real and complex numbers, but rather less about their…

Motivated by finding analogues of elliptic curve point counting techniques, we introduce one deterministic and two new Monte Carlo randomized algorithms to compute the characteristic polynomial of a finite rank-two Drinfeld module. We…

Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a…

Given a central integral arrangement, the reduction of the arrangement modulo positive integers $q$ gives rise to a subgroup arrangement in $(\mathbb{Z}/q\mathbb{Z})^\ell$. Kamiya-Takemura-Terao (2008) introduced the notion of…

The colored Jones polynomial is a knot invariant that plays a central role in low dimensional topology. We give a simple and an efficient algorithm to compute the colored Jones polynomial of any knot. Our algorithm utilizes the walks along…

In this note we compute some enumerative invariants of real and complex projective spaces by means of some enriched graphs called floor diagrams.

This note is dedicated to the study of a Hopf module structures on the space of framed chord diagrams and framed graphs. We also introduce a framed version of the chromatic polynomial and propose two methods to construct framed weight…

We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges…

We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…

Graph colorings is a fundamental topic in graph theory that require an assignment of labels (or colors) to vertices or edges subject to various constraints. We focus on the harmonious coloring of a graph, which is a proper vertex coloring…

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in…