Related papers: Graph Coloring Using Heat Diffusion
Answer Set Programming (ASP) is a famous logic language for knowledge representation, which has been really successful in the last years, as witnessed by the great interest into the development of efficient solvers for ASP. Yet, the great…
Burning and cooling are diffusion processes on graphs in which burned (or cooled) vertices spread to their neighbors with a new source picked at discrete time steps. In burning, the one tries to burn the graph as fast as possible, while in…
The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires…
We introduce learning augmented algorithms to the online graph coloring problem. Although the simple greedy algorithm FirstFit is known to perform poorly in the worst case, we are able to establish a relationship between the structure of…
The aim of this paper is to give a systematic mathematical interpretation of the diffusion problem on which Graph Neural Networks (GNNs) models are based. The starting point of our approach is a dissipative functional leading to dynamical…
We consider the single-conflict coloring problem, a graph coloring problem in which each edge of a graph receives a forbidden ordered color pair. The task is to find a vertex coloring such that no two adjacent vertices receive a pair of…
A proper coloring of vertices of a graph is equitable if the sizes of any two color classes differ by at most 1. Such colorings have many applications and are interesting by themselves. In this paper, we discuss the state of art and…
Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…
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…
Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is…
The graph colouring problem consists of assigning labels, or colours, to the vertices of a graph such that no two adjacent vertices share the same colour. In this work we investigate whether deep reinforcement learning can be used to…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
We develop a heuristic graph coloring approximation algorithm that uses the D-Wave 2X as an independent set sampler and evaluate its performance against a fully classical implementation. A randomly generated set of small but hard graph…
Heat diffusion describes the process by which heat flows from areas with higher temperatures to ones with lower temperatures. This concept was previously adapted to graph structures, whereby heat flows between nodes of a graph depending on…
Graph coloring is used in wireless networks to optimize network resources: bandwidth and energy. Nodes access the medium according to their color. It is the responsibility of the coloring algorithm to ensure that interfering nodes do not…
Coloring problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this…
This paper introduces a novel method for image colorization that utilizes a color transformer and generative adversarial networks (GANs) to address the challenge of generating visually appealing colorized images. Conventional approaches…
We propose Generative Probabilistic Image Colorization, a diffusion-based generative process that trains a sequence of probabilistic models to reverse each step of noise corruption. Given a line-drawing image as input, our method suggests…
The problem of inpainting involves reconstructing the missing areas of an image. Inpainting has many applications, such as reconstructing old damaged photographs or removing obfuscations from images. In this paper we present the directional…
In this paper, we consider the problem of a star coloring. In general case the problems in NP-complete. We establish the star chromatic number for splitting graph of complete and complete bipartite graphs, as well of paths and cycles. Our…