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We give a new randomized distributed algorithm for $(\Delta+1)$-coloring in the LOCAL model, running in $O(\sqrt{\log \Delta})+ 2^{O(\sqrt{\log \log n})}$ rounds in a graph of maximum degree~$\Delta$. This implies that the…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris , Johannes Schneider , Hsin-Hao Su

In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…

Data Structures and Algorithms · Computer Science 2023-02-02 Leon Kellerhals , Tomohiro Koana , Pascal Kunz , Rolf Niedermeier

We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…

Data Structures and Algorithms · Computer Science 2026-05-21 Keren Censor-Hillel , Aditi Dudeja , George Giakkoupis

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…

Discrete Mathematics · Computer Science 2026-04-17 Nicolas Bousquet , Antoine Dailly , Eric Duchene , Hamamache Kheddouci , Aline Parreau

Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…

Numerical Analysis · Mathematics 2017-12-19 Eleonora Andreotti , Dominik Edelmann , Nicola Guglielmi , Christian Lubich

Over the past decade, a long line of research has investigated the distributed complexity landscape of locally checkable labeling (LCL) problems on bounded-degree graphs, culminating in an almost-complete classification on general graphs…

Data Structures and Algorithms · Computer Science 2024-02-16 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti , Gustav Schmid

In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-06-14 Pierre Fraigniaud , Pedro Montealegre , Dennis Olivetti , Ivan Rapaport , Ioan Todinca

The semistrong edge coloring, as a relaxation of the well-known strong edge coloring, can be used to model efficient communication scheduling in wireless networks. An edge coloring of a graph $G$ is called \emph{semistrong} if every color…

Combinatorics · Mathematics 2026-05-12 Yuquan Lin , Wensong Lin

A graph coloring has bounded clustering if each monochromatic component has bounded size. This paper studies such a coloring, where the number of colors depends on an excluded complete bipartite subgraph. This is a much weaker assumption…

Combinatorics · Mathematics 2022-09-29 Chun-Hung Liu , David R. Wood

In the Minimum Bisection problem, input is a graph $G$ and the goal is to partition the vertex set into two parts $A$ and $B$, such that $||A|-|B|| \le 1$ and the number $k$ of edges between $A$ and $B$ is minimized. This problem can be…

Data Structures and Algorithms · Computer Science 2023-08-22 Tanmay Inamdar , Daniel Lokshtanov , Saket Saurabh , Vaishali Surianarayanan

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

The present paper studies local distributed graph problems in highly dynamic networks. Communication and changes of the graph happen in synchronous rounds and our algorithms always, i.e., in every round, satisfy non-trivial guarantees, no…

Data Structures and Algorithms · Computer Science 2018-12-10 Philipp Bamberger , Fabian Kuhn , Yannic Maus

We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…

Discrete Mathematics · Computer Science 2012-11-06 Ajit Diwan , Soumitra Pal , Abhiram Ranade

We study graph coloring problems in the streaming model, where the goal is to process an $n$-vertex graph whose edges arrive in a stream, using a limited space that is smaller than the trivial $O(n^2)$ bound. While prior work has largely…

Data Structures and Algorithms · Computer Science 2025-10-22 Sepehr Assadi , Janani Sundaresan , Helia Yazdanyar

The Colouring problem asks whether the vertices of a graph can be coloured with at most $k$ colours for a given integer $k$ in such a way that no two adjacent vertices receive the same colour. A graph is $(H_1,H_2)$-free if it has no…

Computational Complexity · Computer Science 2017-12-08 Konrad Dabrowski , Daniel Paulusma

An edge-locating coloring of a simple connected graph $G$ is a partition of its edge set into matchings such that the vertices of $G$ are distinguished by the distance to the matchings. The minimum number of the matchings of $G$ that admits…

Combinatorics · Mathematics 2023-10-10 M. Korivand , D. A. Mojdeh , Edy Tri Baskoro , A. Erfanian

In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-12-24 Mika Göös , Juho Hirvonen , Jukka Suomela

One of the central models in distributed computing is Linial's LOCAL model [SIAM J. Comp. 1992]. Over time, researchers have studied distributed graph problems in the LOCAL model under slightly different assumptions, such as whether nodes…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-14 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti , Timothé Picavet , Gustav Schmid

We consider vertex colorings of graphs in which adjacent vertices have distinct colors. A graph is $s$-chromatic if it is colorable in $s$ colors and any coloring of it uses at least $s$ colors. The forcing chromatic number $F(G)$ of an…

Computational Complexity · Computer Science 2007-05-23 Frank Harary , Wolfgang Slany , Oleg Verbitsky

In this paper we consider coloring problems on graphs and other combinatorial structures on standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings can be made well-behaved in the sense of topology or…

Combinatorics · Mathematics 2023-07-19 Anton Bernshteyn