Related papers: Improved upper and lower bound techniques for mono…
In this work we start the investigation of tight complexity bounds for connectivity problems parameterized by cutwidth assuming the Strong Exponential-Time Hypothesis (SETH). Van Geffen et al. posed this question for odd cycle transversal…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…
In this paper, a necessary and sufficient condition for the controllability of networked systems with heterogeneous dynamics is established where the nodes are higher dimensional linear time invariant systems and the network topology is…
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…
The widespread adoption of deep learning is often attributed to its automatic feature construction with minimal inductive bias. However, in many real-world tasks, the learned function is intended to satisfy domain-specific constraints. We…
We consider intrinsic linking and knotting in the context of directed graphs. We construct an example of a directed graph that contains a consistently oriented knotted cycle in every embedding. We also construct examples of intrinsically…
This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph.…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
A graph class is monotone if it is closed under taking subgraphs. It is known that a monotone class defined by finitely many obstructions has bounded treewidth if and only if one of the obstructions is a so-called tripod, that is, a…
In this paper, we study the notions of connected domination number and of outer-connected domination number for middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph M(G). We also compute the…
We consider discrete sine-Gordon equation on branched domains. The latter is modeled in terms of the metric graphs with discrete bonds having the form of the branched 1D chains. Exact analytical solutions of the problem are obtained for…
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…
Smoothed analysis is a framework suggested for mediating gaps between worst-case and average-case complexities. In a recent work, Dinitz et al.~[Distributed Computing, 2018] suggested to use smoothed analysis in order to study dynamic…
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…
In this paper we study the rank of planar rigidity matrix of 4-valent graphs, both in case of generic realizations and configurations in general position, under various connectivity assumptions on the graphs. For each case considered, we…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…