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We present a simple randomized algorithm that can efficiently maintain a $(\Delta+1)$ coloring as the graph undergoes edge insertion and deletion updates, where $\Delta$ denotes an upper bound on the maximum degree. A key advantage is the…

Data Structures and Algorithms · Computer Science 2025-12-11 Mohsen Ghaffari , Jaehyun Koo

We present a new approach to randomized distributed graph coloring that is simpler and more efficient than previous ones. In particular, it allows us to tackle the $(\operatorname{deg}+1)$-list-coloring (D1LC) problem, where each node $v$…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-12-02 Magnús M. Halldórsson , Fabian Kuhn , Alexandre Nolin , Tigran Tonoyan

Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-06-17 Maxime Flin , Magnus M. Halldorsson , Alexandre Nolin

We consider the distributed complexity of the (degree+1)-list coloring problem, in which each node $u$ of degree $d(u)$ is assigned a palette of $d(u)+1$ colors, and the goal is to find a proper coloring using these color palettes. The…

Data Structures and Algorithms · Computer Science 2026-03-18 Sam Coy , Artur Czumaj , Peter Davies , Gopinath Mishra

In this paper, we consider algorithms for edge-coloring multigraphs $G$ of bounded maximum degree, i.e., $\Delta(G) = O(1)$. Shannon's theorem states that any multigraph of maximum degree $\Delta$ can be properly edge-colored with…

Data Structures and Algorithms · Computer Science 2023-10-31 Abhishek Dhawan

Graph coloring is one of the central problems in distributed graph algorithms. Much of the research on this topic has focused on coloring with $\Delta+1$ colors, where $\Delta$ denotes the maximum degree. Using $\Delta+1$ colors may be…

Data Structures and Algorithms · Computer Science 2017-08-24 Mohsen Ghaffari , Christiana Lymouri

Coloring unit-disk graphs efficiently is an important problem in the global and distributed setting, with applications in radio channel assignment problems when the communication relies on omni-directional antennas of the same power. In…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-01-23 Louis Esperet , Sébastien Julliot , Arnaud de Mesmay

In this paper we present a deterministic CONGEST algorithm to compute an $O(k\Delta)$-vertex coloring in $O(\Delta/k)+\log^* n$ rounds, where $\Delta$ is the maximum degree of the network graph and $1\leq k\leq O(\Delta)$ can be freely…

Data Structures and Algorithms · Computer Science 2023-02-28 Yannic Maus

A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A connected graph $G$ is said to be $t$-admissible if admits a special spanning tree in which the distance between any two adjacent vertices…

Combinatorics · Mathematics 2024-06-13 Fernanda Couto , Diego Amaro Ferraz , Sulamita Klein

We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for $(\Delta+1)$- vertex coloring and…

Data Structures and Algorithms · Computer Science 2017-11-15 Sayan Bhattacharya , Deeparnab Chakrabarty , Monika Henzinger , Danupon Nanongkai

Given a dynamic graph $G$ with $n$ vertices and $m$ edges subject to insertion an deletions of edges, we show how to maintain a $(1+\varepsilon)\Delta$-edge-colouring of $G$ without the use of randomisation. More specifically, we show a…

Data Structures and Algorithms · Computer Science 2025-11-10 Aleksander B. G. Christiansen

We consider the problem of maintaining a proper $(\Delta + 1)$-vertex coloring in a graph on $n$-vertices and maximum degree $\Delta$ undergoing edge insertions and deletions. We give a randomized algorithm with amortized update time…

Data Structures and Algorithms · Computer Science 2025-07-08 Maxime Flin , Magnús M. Halldórsson

We give a new randomized distributed algorithm for the $\Delta+1$-list coloring problem. The algorithm and its analysis dramatically simplify the previous best result known of Chang, Li, and Pettie [SICOMP 2020]. This allows for numerous…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-05-12 Magnús M. Halldórsson , Alexandre Nolin , Tigran Tonoyan

One of the fundamental open problems in the area of distributed graph algorithms is the question of whether randomization is needed for efficient symmetry breaking. While there are fast, $\text{poly}\log n$-time randomized distributed…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-05-29 Philipp Bamberger , Mohsen Ghaffari , Fabian Kuhn , Yannic Maus , Jara Uitto

Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-07-28 Ahmet Erdem Sarıyüce , Erik Saule , Ümit V. Çatalyürek

The distributed (Delta + 1)-coloring problem is one of most fundamental and well-studied problems of Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms…

Distributed, Parallel, and Cluster Computing · Computer Science 2008-12-26 Leonid Barenboim , Michael Elkin

We study the edge-colouring problem, and give efficient algorithms where the number of colours is parameterised by the graph's arboricity, $\alpha$. In a dynamic graph, subject to insertions and deletions, we give a deterministic algorithm…

Data Structures and Algorithms · Computer Science 2025-01-15 Aleksander B. G. Christiansen , Eva Rotenberg , Juliette Vlieghe

The problem of edge coloring has been extensively studied over the years. Recently, this problem has received significant attention in the dynamic setting, where we are given a dynamic graph evolving via a sequence of edge insertions and…

Data Structures and Algorithms · Computer Science 2024-02-08 Sayan Bhattacharya , Martín Costa , Nadav Panski , Shay Solomon

We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems…

Combinatorics · Mathematics 2025-06-11 Claudia Archetti , Martina Cerulli , Carmine Sorgente

A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A connected graph $G$ is said to be $t$-admissible if admits a spanning tree in which the distance between any two adjacent vertices of $G$…

Combinatorics · Mathematics 2024-11-05 Fernanda Couto , Diego Amaro Ferraz , Sulamita Klein