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We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of…

Combinatorics · Mathematics 2025-09-03 Michal Dvořák , Dušan Knop , Michal Opler , Jan Pokorný , Ondřej Suchý , Krisztina Szilágyi

The intersection graph induced by a set $\Disks$ of $n$ disks can be dense. It is thus natural to try and sparsify it, while preserving connectivity. Unfortunately, sparse graphs can always be made disconnected by removing a small number of…

Computational Geometry · Computer Science 2022-01-07 Sariel Har-Peled , Eliot Wong Robson

Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrary planar graph to index the decomposition. We prove that…

Combinatorics · Mathematics 2007-06-13 David R. Wood , Jan Arne Telle

Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…

Machine Learning · Statistics 2017-08-31 Martin Sundin , Arun Venkitaraman , Magnus Jansson , Saikat Chatterjee

Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…

Urban mobility forecast and analysis can be addressed through grid-based and graph-based models. However, graph-based representations have the advantage of more realistically depicting the mobility networks and being more robust since they…

Discrete Mathematics · Computer Science 2023-10-11 Rafael Martínez Márquez , Giuseppe Patanè

Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…

Data Structures and Algorithms · Computer Science 2021-08-11 Alexander Noe

Inferring missing links or detecting spurious ones based on observed graphs, known as link prediction, is a long-standing challenge in graph data analysis. With the recent advances in deep learning, graph neural networks have been used for…

Social and Information Networks · Computer Science 2023-01-03 Xingping Xian , Tao Wu , Xiaoke Ma , Shaojie Qiao , Yabin Shao , Chao Wang , Lin Yuan , Yu Wu

We present compact distributed interactive proofs for the recognition of two important graph classes, well-studied in the context of centralized algorithms, namely complement reducible graphs and distance-hereditary graphs. Complement…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-12-08 Pedro Montealegre , Diego Ramírez-Romero , Iván Rapaport

In fault-tolerant distance labeling we wish to assign short labels to the vertices of a graph $G$ such that from the labels of any three vertices $u,v,f$ we can infer the $u$-to-$v$ distance in the graph $G\setminus \{f\}$. We show that any…

Data Structures and Algorithms · Computer Science 2021-02-16 Aviv Bar-Natan , Panagiotis Charalampopoulos , Paweł Gawrychowski , Shay Mozes , Oren Weimann

Graphs are widespread data structures used to model a wide variety of problems. The sheer amount of data to be processed has prompted the creation of a myriad of systems that help us cope with massive scale graphs. The pressure to deliver…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-10-09 Luis M. Vaquero , Felix Cuadrado , Matei Ripeanu

Streets networks provide an invaluable source of information about the different temporal and spatial patterns emerging in our cities. These streets are often represented as graphs where intersections are modelled as nodes and streets as…

Machine Learning · Statistics 2022-11-10 Mateo Neira , Roberto Murcio

Due to their capacity to encode rich structural information, labeled graphs are often used for modeling various kinds of objects such as images, molecules, and chemical compounds. If pattern recognition problems such as clustering and…

Data Structures and Algorithms · Computer Science 2019-08-02 David B. Blumenthal

In this work, we study conditions for the existence of length-constrained path-cycle decompositions, that is, partitions of the edge set of a graph into paths and cycles of a given minimum length. Our main contribution is the…

Combinatorics · Mathematics 2023-06-22 Andrea Jiménez , Yoshiko Wakabayashi

Finding dense subgraphs is a core problem in graph mining with many applications in diverse domains. At the same time many real-world networks vary over time, that is, the dataset can be represented as a sequence of graph snapshots. Hence,…

Data Structures and Algorithms · Computer Science 2023-08-31 Chamalee Wickrama Arachchi , Nikolaj Tatti

The search for linguistic patterns, stylometry and forensic linguistics have in the theory of complex networks, their structures and associated mathematical tools, allies with which to model and analyze texts. In this paper we present a new…

Combinatorics · Mathematics 2022-09-14 Angeles Criado-Alonso , David Aleja , Miguel Romance , Regino Criado

Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…

Metric Geometry · Mathematics 2023-02-06 Samir Chowdhury , Tom Needham , Ethan Semrad , Bei Wang , Youjia Zhou

Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…

Machine Learning · Computer Science 2023-05-16 Yanping Zheng , Zhewei Wei , Jiajun Liu

Isocontours in road networks represent the area that is reachable from a source within a given resource limit. We study the problem of computing accurate isocontours in realistic, large-scale networks. We propose polygons with minimum…

Data Structures and Algorithms · Computer Science 2016-02-05 Moritz Baum , Thomas Bläsius , Andreas Gemsa , Ignaz Rutter , Franziska Wegner

We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all…

Combinatorics · Mathematics 2026-03-10 András Gyárfás , Márton Marits , Géza Tóth