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A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in…

Combinatorics · Mathematics 2023-06-06 Kai Siong Yow , Ningyi Liao , Siqiang Luo , Reynold Cheng , Chenhao Ma , Xiaolin Han

A Helly circular-arc graph is the intersection graph of a set of arcs on a circle having the Helly property. We introduce essential obstacles, which are a refinement of the notion of obstacles, and prove that essential obstacles are…

Combinatorics · Mathematics 2021-08-31 Martín D. Safe

In recent years, a growing number of method and application works have adapted and applied the causal-graphical-model framework to time series data. Many of these works employ time-resolved causal graphs that extend infinitely into the past…

Statistics Theory · Mathematics 2023-10-10 Andreas Gerhardus , Jonas Wahl , Sofia Faltenbacher , Urmi Ninad , Jakob Runge

Vertex connectivity and its variants are among the most fundamental problems in graph theory, with decades of extensive study and numerous algorithmic advances. The directed variants of vertex connectivity are usually solved by manually…

Data Structures and Algorithms · Computer Science 2025-10-24 Olivier Fischer , Yonggang Jiang , Sagnik Mukhopadhyay , Sorrachai Yingchareonthawornchai

We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…

Data Structures and Algorithms · Computer Science 2025-12-17 Ron Mosenzon

We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…

Data Structures and Algorithms · Computer Science 2020-12-01 Amit Levi , Ramesh Krishnan S. Pallavoor , Sofya Raskhodnikova , Nithin Varma

Graph representation learning (also known as network embedding) has been extensively researched with varying levels of granularity, ranging from nodes to graphs. While most prior work in this area focuses on node-level representation,…

Machine Learning · Computer Science 2023-06-05 Lili Wang , Chenghan Huang , Weicheng Ma , Xinyuan Cao , Soroush Vosoughi

For a graph class $\mathcal{C}$, the $\mathcal{C}$-Edge-Deletion problem asks for a given graph $G$ to delete the minimum number of edges from $G$ in order to obtain a graph in $\mathcal{C}$. We study the $\mathcal{C}$-Edge-Deletion problem…

Data Structures and Algorithms · Computer Science 2021-11-15 Toshiki Saitoh , Ryo Yoshinaka , Hans L. Bodlaender

We prove the following theorem. Given a planar graph $G$ and an integer $k$, it is possible in polynomial time to randomly sample a subset $A$ of vertices of $G$ with the following properties: (i) $A$ induces a subgraph of $G$ of treewidth…

Data Structures and Algorithms · Computer Science 2016-04-21 Fedor V. Fomin , Daniel Lokshtanov , Dániel Marx , Marcin Pilipczuk , Michał Pilipczuk , Saket Saurabh

Graphs are becoming one of the most popular data modeling paradigms since they are able to model complex relationships that cannot be easily captured using traditional data models. One of the major tasks of graph management is graph…

Databases · Computer Science 2013-11-12 Carlos R. Rivero , Hasan M. Jamil

We report on a recent breakthrough in rule-based graph programming, which allows us to reach the time complexity of imperative linear-time algorithms. In general, achieving the complexity of graph algorithms in conventional languages using…

Programming Languages · Computer Science 2025-03-27 Ziad Ismaili Alaoui , Detlef Plump

We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, {\sc $k$-Leaf…

Data Structures and Algorithms · Computer Science 2010-01-07 Frederic Dorn , Fedor V. Fomin , Daniel Lokshtanov , Venkatesh Raman , Saket Saurabh

In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…

Discrete Mathematics · Computer Science 2008-04-23 Rico Zenklusen

Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…

Data Structures and Algorithms · Computer Science 2016-11-24 Éric Colin de Verdière

We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…

Computational Geometry · Computer Science 2020-12-18 Mark de Berg , Hans L. Bodlaender , Sándor Kisfaludi-Bak , Dániel Marx , Tom C. van der Zanden

The girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as distributed computing, girth-related problems have been object of attention in both past and…

Data Structures and Algorithms · Computer Science 2018-09-21 Kazuhiro Kurita , Kunihiro Wasa , Alessio Conte , Hiroki Arimura , Takeaki Uno

Counting small patterns in a large dataset is a fundamental algorithmic task. The most common version of this task is subgraph/homomorphism counting, wherein we count the number of occurrences of a small pattern graph $H$ in an input graph…

Data Structures and Algorithms · Computer Science 2025-10-21 Daniel Paul-Pena , C. Seshadhri

The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics. Many hard computational problems on graphs turn out to be efficiently solvable in…

Data Structures and Algorithms · Computer Science 2019-09-24 Michał Ziobro , Marcin Pilipczuk

Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case.…

Data Structures and Algorithms · Computer Science 2023-08-01 Noga Alon , Allan Grønlund , Søren Fuglede Jørgensen , Kasper Green Larsen

Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…

Computational Geometry · Computer Science 2019-03-13 Benjamin Niedermann , Ignaz Rutter , Matthias Wolf