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Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…

Data Structures and Algorithms · Computer Science 2019-09-02 Suprovat Ghoshal , Anand Louis , Rahul Raychaudhury

A matching is a set of edges in a graph with no common endpoint. A matching M is called acyclic if the induced subgraph on the endpoints of the edges in M is acyclic. Given a graph G and an integer k, Acyclic Matching Problem seeks for an…

Computational Complexity · Computer Science 2022-10-05 Sahab Hajebi , Ramin Javadi

A proper vertex coloring of a graph is a mapping of its vertices on a set of colors, such that two adjacent vertices are not mapped to the same color. This constraint may be interpreted in terms of the distance between to vertices and so a…

Combinatorics · Mathematics 2017-11-10 Sebastian Wiederrecht

For a simple graph G = (V, E) and a positive integer k greater than or equal to 2, a coloring of vertices of G using exactly k colors such that each vertex has an equal number of neighbors of each color is called neighborhood-balanced…

Combinatorics · Mathematics 2025-09-09 Maurice Genevieva Almeida , Tarkeshwar Singh , Siddharth Gupta , Ravindra Pawar

Irregular computations on unstructured data are an important class of problems for parallel programming. Graph coloring is often an important preprocessing step, e.g. as a way to perform dependency analysis for safe parallel execution. The…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-19 Georgios Rokos , Gerard Gorman , Paul H J Kelly

Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…

Data Structures and Algorithms · Computer Science 2021-12-24 Ashwin Jacob , Jari J. H. de Kroon , Diptapriyo Majumdar , Venkatesh Raman

Coloring is one of the most famous problems in graph theory. The coloring problem on undirected graphs has been well studied, whereas there are very few results for coloring problems on directed graphs. An oriented k-coloring of an oriented…

Data Structures and Algorithms · Computer Science 2019-06-12 Frank Gurski , Dominique Komander , Carolin Rehs

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…

Statistical Mechanics · Physics 2009-11-07 R. Mulet , A. Pagnani , M. Weigt , R. Zecchina

Graph coloring, also known as vertex coloring, considers the problem of assigning colors to the nodes of a graph such that adjacent nodes do not share the same color. The optimization version of the problem concerns the minimization of the…

Artificial Intelligence · Computer Science 2010-11-25 Hugo Hernández , Christian Blum

Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with…

Computational Geometry · Computer Science 2016-09-06 Jaakko Peltonen , Ziyuan Lin

Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…

Computational Complexity · Computer Science 2022-12-20 Falko Hegerfeld , Stefan Kratsch

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…

Combinatorics · Mathematics 2021-03-16 András London , Ryan R. Martin , András Pluhár

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…

Combinatorics · Mathematics 2026-03-16 Peter Bradshaw , Tomáš Masařík

For a simple graph G = (V, E), a coloring of vertices of G using two colors, say red and blue, is called a quasi neighborhood balanced coloring if, for every vertex of the graph, the number of red neighbors and the number of blue neighbors…

Combinatorics · Mathematics 2026-05-18 Maurice Genevieva Almeida

In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly $90^\circ$, where the number of bends on such polylines is typically restricted in some way.…

Computational Geometry · Computer Science 2023-08-24 Cornelius Brand , Robert Ganian , Sebastian Röder , Florian Schager

Inspired by the majority colorings and C-colorings, we introduce and study the majority C-coloring of graphs. In such a vertex coloring, every vertex shares its color with at least half of its neighbors. The maximum number of colors that…

Combinatorics · Mathematics 2026-04-23 Csilla Bujtas , Magda Dettlaff , Hanna Furmanczyk , Aleksandra Laskowska

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…

Statistical Mechanics · Physics 2009-11-11 S. Bounkong , J. van Mourik , D. Saad

In an undirected graph, a proper (k,i)-coloring is an assignment of a set of k colors to each vertex such that any two adjacent vertices have at most i common colors. The (k,i)-coloring problem is to compute the minimum number of colors…

Data Structures and Algorithms · Computer Science 2020-09-14 Sriram Bhyravarapu , Saurabh Joshi , Subrahmanyam Kalyanasundaram , Anjeneya Swami Kare

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…

Combinatorics · Mathematics 2021-08-13 Michał Dębski , Stefan Felsner , Piotr Micek , Felix Schröder

Let $\partial_H(u)$ be the set of edges incident with a vertex $u$ in the graph $H$. We say that a graph $G$ is $H$-colorable if there exist total functions $f : E(G) \rightarrow E(H)$ and $g : V(G) \rightarrow V(H)$ such that $f$ is a…

Combinatorics · Mathematics 2024-01-12 Jorik Jooken