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Related papers: Local certification of forbidden subgraphs

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A proof-labeling scheme (PLS) for a boolean predicate $\Pi$ on labeled graphs is a mechanism used for certifying the legality with respect to $\Pi$ of global network states in a distributed manner. In a PLS, a certificate is assigned to…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-07-27 Pierre Fraigniaud , Frédéric Mazoit , Pedro Montealegre , Ivan Rapaport , Ioan Todinca

In this work we study local computation with advice: the goal is to solve a graph problem $\Pi$ with a distributed algorithm in $T(\Delta)$ communication rounds, for some function $T$ that only depends on the maximum degree $\Delta$ of the…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-25 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Krzysztof Nowicki , Dennis Olivetti , Eva Rotenberg , Jukka Suomela

Local sets, a graph structure invariant under local complementation, have been originally introduced in the context of quantum computing for the study of quantum entanglement within the so-called graph state formalism. A local set in a…

Quantum Physics · Physics 2025-09-09 Nathan Claudet , Simon Perdrix

We consider graph property testing in $p$-degenerate graphs under the random neighbor oracle model (Czumaj and Sohler, FOCS 2019). In this framework, a tester explores a graph by sampling uniform neighbors of vertices, and a property is…

Data Structures and Algorithms · Computer Science 2026-04-07 Oded Lachish , Amit Levi , Ilan Newman , Felix Reidl

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider this problem in the setting of local algorithms: one wants to quickly determine whether a given edge $e$ is in a specific spanning tree,…

Data Structures and Algorithms · Computer Science 2021-04-28 Reut Levi , Dana Ron , Ronitt Rubinfeld

A local subgraph of a graph is the subgraph induced by the neighborhood of a vertex. Thus a graph of order $n$ has $n$ local subgraphs. A graph $G$ is called locally nonforesty if every local subgraph of $G$ contains a cycle. Recently, in…

Combinatorics · Mathematics 2024-11-01 Chengli Li , Yurui Tang , Xingzhi Zhan

In the Online Delayed Connected H-Node-Deletion Problem, an unweighted graph is revealed vertex by vertex and it must remain free of any induced copies of a specific connected induced forbidden subgraph H at each point in time. To achieve…

Data Structures and Algorithms · Computer Science 2025-01-27 Hans-Joachim Böckenhauer , Melvin Jahn , Dennis Komm , Moritz Stocker

Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…

Statistics Theory · Mathematics 2020-06-30 P-A. Maugis

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

Computational Physics · Physics 2009-11-13 Lucas Antiqueira , Luciano da Fontoura Costa

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

We study the {\em verification} problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would like to verify whether $H$ has some…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-10-18 Atish Das Sarma , Stephan Holzer , Liah Kor , Amos Korman , Danupon Nanongkai , Gopal Pandurangan , David Peleg , Roger Wattenhofer

Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in…

Data Structures and Algorithms · Computer Science 2025-08-25 Yi-Jun Chang , Lyuting Chen , Yanyu Chen , Gopinath Mishra , Mingyang Yang

In this work we study the cost of local and global proofs on distributed verification. In this setting the nodes of a distributed system are provided with a nondeterministic proof for the correctness of the state of the system, and the…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-03-28 Laurent Feuilloley , Juho Hirvonen

A graph is locally chordal if each of its small-radius balls is chordal. In an earlier work [AKK25], the authors and Kobler proved that locally chordal graphs can be characterized by having chordal local covers, by forbidding short cycles…

Combinatorics · Mathematics 2025-12-23 Tara Abrishami , Paul Knappe

Network detection is an important capability in many areas of applied research in which data can be represented as a graph of entities and relationships. Oftentimes the object of interest is a relatively small subgraph in an enormous,…

Social and Information Networks · Computer Science 2018-04-12 Steven T. Smith , Kenneth D. Senne , Scott Philips , Edward K. Kao , Garrett Bernstein

A signed graph (SG) is a graph where edges carry sign information attached to it. The sign of a network can be positive, negative, or neutral. A signed network is ubiquitous in a real-world network like social networks, citation networks,…

Social and Information Networks · Computer Science 2024-09-09 Shrabani Ghosh

We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis,…

Statistics Theory · Mathematics 2013-03-01 Ery Arias-Castro , Nicolas Verzelen

In this paper, we present a 2-local proof labeling scheme with labels in $\{ 0,1,2\}$ for leader election in anonymous meshed graphs. Meshed graphs form a general class of graphs defined by a distance condition. They comprise several…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-16 Jérémie Chalopin , Victor Chepoi , Maria Kokkou

This paper presents a simple and efficient approach for finding the bridges and failure points in a densely connected network mapped as a graph. The algorithm presented here is a parallel algorithm which works in a distributed environment.…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-08-18 Ashwani Kumar , Aditya Pratap Singh

A popular way to define or characterize graph classes is via forbidden subgraphs or forbidden minors. These characterizations play a key role in graph theory, but they rarely lead to efficient algorithms to recognize these classes. In…

Data Structures and Algorithms · Computer Science 2023-02-24 Guillaume Ducoffe , Laurent Feuilloley , Michel Habib , François Pitois