Related papers: A simple linear-time algorithm for generating auxi…
We study the 2-edge-connected spanning subgraph (2-ECSS) problem: Given a graph $G$, compute a connected subgraph $H$ of $G$ with the minimum number of edges such that $H$ is spanning, i.e., $V(H) = V(G)$, and $H$ is 2-edge-connected, i.e.,…
Complex networks often exhibit community structure, with communities corresponding to denser subgraphs in which nodes are closely linked. When modelling systems where interactions extend beyond node pairs to arbitrary numbers of nodes,…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second…
When searching for interesting structures in graphs, it is often important to take into account not only the graph connectivity, but also the metadata available, such as node and edge labels, or temporal information. In this paper we are…
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between…
We introduce a new concept of a subgraph class called a superbubble for analyzing assembly graphs, and propose an efficient algorithm for detecting it. Most assembly algorithms utilize assembly graphs like the de Bruijn graph or the overlap…
Counting and finding triangles in graphs is often used in real-world analytics to characterize cohesiveness and identify communities in graphs. In this paper, we propose the novel concept of a cover-edge set that can be used to find…
The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining,…
We are developing an interactive graph exploration system called Graph Playground for making sense of large graphs. Graph Playground offers a fast and scalable edge decomposition algorithm, based on iterative vertex-edge peeling, to…
Induced bipartite subgraphs of maximal vertex cardinality are an essential concept for the analysis of graphs. Yet, discovering them in large graphs is known to be computationally hard. Therefore, we consider in this work a weaker notion of…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…
A set $X$ of vertices of an acyclic digraph $D$ is convex if $X\neq \emptyset$ and there is no directed path between vertices of $X$ which contains a vertex not in $X$. A set $X$ is connected if $X\neq \emptyset$ and the underlying…
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
Many graph problems can be solved using ordered parallel graph algorithms that achieve significant speedup over their unordered counterparts by reducing redundant work. This paper introduces a new priority-based extension to GraphIt, a…
This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are…
A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was…
2-joins are edge cutsets that naturally appear in the decomposition of several classes of graphs closed under taking induced subgraphs, such as balanced bipartite graphs, even-hole-free graphs, perfect graphs and claw-free graphs. Their…
We give a parallel $O(\log(n))$-time algorithm on a CRCW PRAM to assign vertical and horizontal segments to the vertices of any planar bipartite graph $G$ in the following manner: i) Two segments cannot share an interior point ii) Two…
Recently, Kawarabayashi and Thorup presented the first deterministic edge-connectivity recognition algorithm in near-linear time. A crucial step in their algorithm uses the existence of vertex subsets of a simple graph $G$ on $n$ vertices…