Related papers: Color representations of Ising models
Given a graph $G$, we form a random subgraph $G_p$ by including each edge of $G$ independently with probability $p$. We provide an asymptotic expansion of the expected number of independent sets in random subgraphs of regular bipartite…
We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high…
This work presents a comprehensive study of the generalized Duffing oscillator, a fundamental model in nonlinear dynamics described by the system $$ \dot{x} = y, \quad \dot{y} = -\alpha y - \epsilon x^m - \sigma x, $$ where $\epsilon \neq…
A vertex coloring $\phi$ of a graph $G$ is $p$-centered if for every connected subgraph $H$ of $G$ either $\phi$ uses more than $p$ colors on $H$ or there is a color that appears exactly once on $H$. Centered colorings form one of the…
We present a graph model for a background independent, relational approach to spacetime emergence. The general idea and the graph main features, detailed in [1], are discussed. This is a combinatorial (dynamical) metric graph, colored on…
A matrix \( A \) is called \emph{kernel partition regular} if, for every finite coloring of the natural numbers \( \mathbb{N} \), there exists a monochromatic solution to the equation \( A\vec{X} = 0 \). In 1933, Rado characterized such…
A star $k$-edge coloring is a proper edge coloring such that there are no bichromatic paths or cycles of length four. The smallest integer $k$ such that $G$ admits a star $k$-edge coloring is the star chromatic index of $G$. Deng \etal…
A well-studied concept is that of the total chromatic number. A proper total colouring of a graph is a colouring of both vertices and edges so that every pair of adjacent vertices receive different colours, every pair of adjacent edges…
For graphs $G$ and $H$, a homomorphism from $G$ to $H$, or $H$-coloring of $G$, is a map from the vertices of $G$ to the vertices of $H$ that preserves adjacency. When $H$ is composed of an edge with one looped endvertex, an $H$-coloring of…
Consider a graph whose vertices are colored in one of two colors, say black or white. A white vertex is called integrated if it has at least as many black neighbors as white neighbors, and similarly for a black vertex. The coloring as a…
We introduce a variant of the vertex-distinguishing edge coloring problem, where each edge is assigned a subset of colors. The label of a vertex is the union of the sets of colors on edges incident to it. In this paper we investigate the…
We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising models with edge activities $\boldsymbol{\beta} > 1$ and external fields $\boldsymbol{\lambda}<1$ (or symmetrically, $\boldsymbol{\lambda}>1$) on…
A coloring is distinguishing (or symmetry breaking) if no non-identity automorphism preserves it. The distinguishing threshold of a graph $G$, denoted by $\theta(G)$, is the minimum number of colors $k$ so that every $k$-coloring of $G$ is…
Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of…
The chromatic number $\chi(G)$ of a graph $G$, that is, the smallest number of colors required to color the vertices of $G$ so that no two adjacent vertices are assigned the same color, is a classic and extensively studied parameter. Here…
A \emph{proper $t$-edge-coloring} of a graph $G$ is a mapping $\alpha: E(G)\rightarrow \{1,\ldots,t\}$ such that all colors are used, and $\alpha(e)\neq \alpha(e^{\prime})$ for every pair of adjacent edges $e,e^{\prime}\in E(G)$. If $\alpha…
We consider a Schelling model of self-organized segregation in an open system that is equivalent to a zero-temperature Ising model with Glauber dynamics, or an Asynchronous Cellular Automaton (ACA) with extended Moore neighborhoods.…
We investigate the List $H$-Coloring problem, the generalization of graph coloring that asks whether an input graph $G$ admits a homomorphism to the undirected graph $H$ (possibly with loops), such that each vertex $v \in V(G)$ is mapped to…
We give an almost complete characterization of the hardness of $c$-coloring $\chi$-chromatic graphs with distributed algorithms, for a wide range of models of distributed computing. In particular, we show that these problems do not admit…
This is a treatise on finite point configurations spanning a fixed volume to be found in a single color-class of an arbitrary finite (measurable) coloring of the Euclidean space $\mathbb{R}^n$, or in a single large measurable subset…