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In graph coloring problems, the goal is to assign a positive integer color to each vertex of an input graph such that adjacent vertices do not receive the same color assignment. For classic graph coloring, the goal is to minimize the…

Data Structures and Algorithms · Computer Science 2016-10-11 Joan Boyar , Leah Epstein , Lene M. Favrholdt , Kim S. Larsen , Asaf Levin

Given a graph $G=(V,E)$, the $b$-coloring problem consists in attributing a color to every vertex in $V$ such that adjacent vertices receive different colors, every color has a $b$-vertex, and the number of colors is maximized. A $b$-vertex…

Optimization and Control · Mathematics 2021-03-08 Rafael A. Melo , Michell F. Queiroz , Marcio C. Santos

The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that for all vertices v the color of v is different from the color of any of its neighbors. The problem is NP-hard.…

Computational Geometry · Computer Science 2017-07-12 Adalat Jabrayilov , Petra Mutzel

In this paper, we consider the maximum $k$-edge-colorable subgraph problem. In this problem we are given a graph $G$ and a positive integer $k$, the goal is to take $k$ matchings of $G$ such that their union contains maximum number of…

Combinatorics · Mathematics 2025-10-15 Vahan Mkrtchyan

We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph.…

Neural and Evolutionary Computing · Computer Science 2021-05-27 Jakob Bossek , Frank Neumann , Pan Peng , Dirk Sudholt

We consider the selective graph coloring problem, which is a generalization of the classical graph coloring problem. Given a graph together with a partition of its vertex set into clusters, we want to choose exactly one vertex per cluster…

Data Structures and Algorithms · Computer Science 2021-01-01 Oylum Şeker , Tınaz Ekim , Z. Caner Taşkın

Several authors modelled networks ad hoc by oriented or disoriented graphs, whereby the problem of allowance (allocation) of the frequencies at the level of the network was transformed into coloring problem of nodes in the graph. Graph…

Discrete Mathematics · Computer Science 2014-06-06 Ali Mansouri , Mohamed Salim Bouhlel

The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that each two adjacent vertices get different colors. For this NP-hard problem, a variety of integer linear…

Discrete Mathematics · Computer Science 2022-06-29 Adalat Jabrayilov , Petra Mutzel

Graph coloring is a fundamental problem in combinatorics with many applications in practice. In this problem, the vertices in a given graph must be colored by using the least number of colors in such a way that a vertex has a different…

Data Structures and Algorithms · Computer Science 2020-08-27 Arda Asik , Ibrahim Bugra Demir , Berker Demirel , Baris Batuhan Topal , Kamer Kaya

The problems studied in this paper originate from Graph Motif, a problem introduced in 2006 in the context of biological networks. Informally speaking, it consists in deciding if a multiset of colors occurs in a connected subgraph of a…

Computational Complexity · Computer Science 2014-09-11 Romeo Rizzi , Florian Sikora

Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some…

Cryptography and Security · Computer Science 2018-03-16 Yuan Hong , Jaideep Vaidya , Haibing Lu

Petford and Welsh introduced a sequential heuristic algorithm for (approximately) solving the NP-hard graph coloring problem. The algorithm is based on the antivoter model and mimics the behaviour of a physical process based on a…

Combinatorics · Mathematics 2023-09-22 Boštjan Gabrovšek , Janez Žerovnik

Node coloring is the task of assigning colors to the nodes of a graph such that no two adjacent nodes have the same color, while using as few colors as possible. It is the most widely studied instance of graph coloring and of central…

Combinatorics · Mathematics 2026-01-09 Knut Vanderbush , Melanie Weber

Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…

Discrete Mathematics · Computer Science 2019-06-12 George B. Mertzios , Hendrik Molter , Viktor Zamaraev

Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…

Social and Information Networks · Computer Science 2014-08-27 Ryan A. Rossi , Nesreen K. Ahmed

The graph coloring problem (GCP) is a classic combinatorial optimization problem that aims to find the minimum number of colors assigned to vertices of a graph such that no two adjacent vertices receive the same color. GCP has been…

Discrete Mathematics · Computer Science 2025-06-10 Enqiang Zhu , Yu Zhang , Haopeng Sun , Ziqi Wei , Witold Pedrycz , Chanjuan Liu , Jin Xu

This paper studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $n^{1-\epsilon}$ for any $\epsilon > 0$, is NP-hard in static…

Data Structures and Algorithms · Computer Science 2020-06-23 Shay Solomon , Nicole Wein

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

This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the…

Data Structures and Algorithms · Computer Science 2015-12-31 Jonathan Turner

We develop the first parallel graph coloring heuristics with strong theoretical guarantees on work and depth and coloring quality. The key idea is to design a relaxation of the vertex degeneracy order, a well-known graph theory concept, and…

Data Structures and Algorithms · Computer Science 2020-11-12 Maciej Besta , Armon Carigiet , Zur Vonarburg-Shmaria , Kacper Janda , Lukas Gianinazzi , Torsten Hoefler