Related papers: On Intersection Graphs of Graphs and Hypergraphs: …
A hypergraph is said to be $1$-Sperner if for every two hyperedges the smallest of their two set differences is of size one. We present several applications of $1$-Sperner hypergraphs and their structure to graphs. In particular, we…
A normal Helly circular-arc graph is the intersection graph of arcs on a circle of which no three or less arcs cover the whole circle. Lin, Soulignac, and Szwarcfiter [Discrete Appl. Math. 2013] characterized circular-arc graphs that are…
Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination problem), covering the vertex set by cliques (clique covering…
Intersection graphs of planar geometric objects such as intervals, disks, rectangles and pseudo-disks are well studied. Motivated by various applications, Butman et al. in SODA 2007 considered algorithmic questions in intersection graphs of…
This paper develops analityc methods for investigating uniform hypergraphs. Its starting point is the spectral theory of 2-graphs, in particular, the largest and the smallest eigenvalues of 2-graphs. On the one hand, this simple setup is…
A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are…
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…
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…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a…
The minimum $s$-$t$ cut problem in graphs is one of the most fundamental problems in combinatorial optimization, and graph cuts underlie algorithms throughout discrete mathematics, theoretical computer science, operations research, and data…
This work derives an upper bound on the maximum cardinality of a family of graphs on a fixed number of vertices, in which the intersection of every two graphs in that family contains a subgraph that is isomorphic to a specified graph H.…
A graph is a powerful concept for representation of relations between pairs of entities. Data with underlying graph structure can be found across many disciplines and there is a natural desire for understanding such data better. Deep…
Hypergraph offers a framework to depict the multilateral relationships in real-world complex data. Predicting higher-order relationships, i.e hyperedge, becomes a fundamental problem for the full understanding of complicated interactions.…
In the last decade, subgraph detection and enumeration have emerged as a central problem in distributed graph algorithms. This is largely due to the theoretical challenges and practical applications of these problems. In this paper, we…
These lecture notes are on automorphism groups of Cayley graphs and their applications to optimal fault-tolerance of some interconnection networks. We first give an introduction to automorphisms of graphs and an introduction to Cayley…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
A biclique of a graph $G$ is an induced complete bipartite subgraph of $G$ such that neither part is empty. A star is a biclique of $G$ such that one part has exactly one vertex. The star graph of $G$ is the intersection graph of the…
This is a survey of the exciting recent progress made in understanding the complexity of distributed subgraph finding problems. It overviews the results and techniques for assorted variants of subgraph finding problems in various models of…
The ability to model and predict ego-vehicle's surrounding traffic is crucial for autonomous pilots and intelligent driver-assistance systems. Acceleration prediction is important as one of the major components of traffic prediction. This…