Related papers: Lee-Yang phenomena in edge-coloured graph counting
In this paper, we study the problem of partitioning a graph into connected and colored components called blocks. Using bivariate generating functions and combinatorial techniques, we determine the expected number of blocks when the vertices…
We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large deviation form with singularities of the…
An edge labeling of a graph distinguishes neighbors by sets (multisets, resp.), if for any two adjacent vertices $u$ and $v$ the sets (multisets, resp.) of labels appearing on edges incident to $u$ and $v$ are different. In an analogous way…
The local complement G*i of a simple graph G at one of its vertices i is obtained by complementing the subgraph induced by the neighborhood of i and leaving the rest of the graph unchanged. If e={i,j} is an edge of G then G*e=((G*i)*j)*i is…
The study of very large graphs is a prominent theme in modern-day mathematics. In this paper we develop a rigorous foundation for studying the space of finite labelled graphs and their limits. These limiting objects are naturally countable…
The asymmetric coloring number of a graph is the minimum number of colors needed to color its vertices, so that no non-trivial automorphism preserves the color classes. We investigate the asymmetric coloring number of graphs that are…
A subspace arrangement defined by intersections of hyperplanes of the braid arrangement can be encoded by an edge colored hypergraph. It turns out that the characteristic polynomial of this type of subspace arrangement is given by a…
We study an analogue of the classical moment problem in the framework where moments are indexed by graphs instead of natural numbers. We study limit objects of graph sequences where edges are labeled by elements of a topological space.…
In this paper, we will study the chromatic number of Cayley graphs of algebraic groups that arise from algebraic constructions. Using Lang-Weil bound and representation theory of finite simple groups of Lie type, we will establish lower…
For a fixed number of colors, we show that, in node-weighted split graphs, cographs, and graphs of bounded tree-width, one can determine in polynomial time whether a proper list-coloring of the vertices of a graph such that the total weight…
We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomial.
We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…
We survey results and conjectures concerning the zero distribution of chromatic and flow polynomials of graphs, and characteristic polynomials of matroids.
Let G = (V;E) be a simple graph. We consider domination polynomial, matching polynomial and edge cover polynomial of G. Graphs which their polynomials have few roots can give sometimes a very surprising information about the structure of…
Inspired by the 1995 paper of Baake--Grimm--Pisani, we aim to explain the empirical observation that the distribution of Lee--Yang zeros corresponding to a one-dimensional Ising model appears to follow the gap labelling theorem. This…
A general (convex) polytope $P\subset\mathbb R^d$ and its edge-graph $G_P$ can have very distinct symmetry properties. We construct a coloring (of the vertices and edges) of the edge-graph so that the combinatorial symmetry group of the…
We present exact calculations of the partition function of the zero-temperature Potts antiferromagnet (equivalently, the chromatic polynomial) for graphs of arbitrarily great length composed of repeated complete subgraphs $K_b$ with $b=5,6$…
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…
We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state…
In this paper we consider a dynamic Erd\H{o}s-R\'{e}nyi random graph with independent identically distributed edge processes. Our aim is to describe the joint evolution of the entries of a subgraph count vector. The main result of this…