Related papers: Computational Complexity Aspects of Point Visibili…
Let $\mathcal{A}$ be a set of positive numbers. A graph $G$ is called an $\mathcal{A}$-embeddable graph in $\mathbb{R}^d$ if the vertices of $G$ can be positioned in $\mathbb{R}^d$ so that the distance between endpoints of any edge is an…
We completely determine the complexity status of the dominating set problem for hereditary graph classes defined by forbidden induced subgraphs with at most five vertices.
An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in classes…
In this paper, we present three necessary conditions for recognizing point visibility graphs. We show that this recognition problem lies in PSPACE. We state new properties of point visibility graphs along with some known properties that are…
The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…
A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
We define a natural class of graphs by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary. We consider mainly the case of compact connected representing regions, proving two results…
Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…
Given a non empty set $S$ of vertices of a graph, the partiality of a vertex with respect to $S$ is the difference between maximum and minimum of the distances of the vertex to the vertices of $S$. The vertices with minimum partiality…
A dominating set of a graph $G=(V,E)$ is a subset of vertices $S\subseteq V$ such that every vertex $v\in V\setminus S$ has at least one neighbor in set $S$. The corresponding optimization problem is known to be NP-hard. The best known…
In the present paper a novel graph-based approach to the shape decomposition problem is addressed. The shape is appropriately transformed into a visibility graph enriched with local neighborhood information. A two-step diffusion process is…
If $x\in V(G)$, then $S\subseteq V(G)\setminus\{x\}$ is an $x$-visibility set if for any $y\in S$ there exists a shortest $x,y$-path avoiding $S$. The $x$-visibility number $v_x(G)$ is the maximum cardinality of an $x$-visibility set, and…
A set $D$ of vertices in a graph $G$ is a dominating set if every vertex of $G$, which is not in $D$, has a neighbor in $D$. A set of vertices $D$ in $G$ is convex (respectively, isometric), if all vertices in all shortest paths…
A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components. The toughness of a graph is the largest $t$ for which the graph is $t$-tough. A graph is minimally $t$-tough if…
A computational graph in a deep neural network (DNN) denotes a specific data flow diagram (DFD) composed of many tensors and operators. Existing toolkits for visualizing computational graphs are not applicable when the structure is highly…
The learning complexity of special sets of vertices in graphs is studied in the model(s) of exact learning by (extended) equivalence and membership queries. Polynomial-time learning algorithms are described for vertex covers, independent…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
We prove two dichotomy results for detecting long paths as patterns in a given graph. The NP-hard problem Longest Induced Path is to determine the longest induced path in a graph. The NP-hard problem Longest Path Contractibility is to…
The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder:…