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A drawing of a graph is fan-planar if the edges intersecting a common edge $a$ share a vertex $A$ on the same side of $a$. More precisely, orienting $e$ arbitrarily and the other edges towards $A$ results in a consistent orientation of the…

Computational Geometry · Computer Science 2021-08-31 Boris Klemz , Kristin Knorr , Meghana M. Reddy , Felix Schröder

The k-planar graphs, which are (usually with small values of k such as 1, 2, 3) subject to recent intense research, admit a drawing in which edges are allowed to cross, but each one edge is allowed to carry at most k crossings. In recently…

Combinatorics · Mathematics 2024-10-02 Petr Hliněný , Lili Ködmön

In streamed graph drawing, a planar graph, G, is given incrementally as a data stream and a straight-line drawing of G must be updated after each new edge is released. To preserve the mental map, changes to the drawing should be minimized…

Data Structures and Algorithms · Computer Science 2013-09-02 Michael T. Goodrich , Paweł Pszona

Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…

Combinatorics · Mathematics 2026-01-01 David Hartman , Aneta Pokorná , Daniel Trlifaj , Lluís Vena

We study a family of reachability problems under waiting-time restrictions in temporal and vertex-colored temporal graphs. Given a temporal graph and a set of source vertices, we find the set of vertices that are reachable from a source via…

Data Structures and Algorithms · Computer Science 2024-12-04 Suhas Thejaswi , Juho Lauri , Aristides Gionis

Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extending a simple drawing $D(G)$ of a graph $G$ by inserting a…

Computational Geometry · Computer Science 2019-08-27 Alan Arroyo , Martin Derka , Irene Parada

A $k$-coloring of a graph is an assignment of integers between $1$ and $k$ to vertices in the graph such that the endpoints of each edge receive different numbers. We study a local variation of the coloring problem, which imposes further…

Combinatorics · Mathematics 2018-09-24 Jie You , Yixin Cao , Jianxin Wang

In this paper, we study the {\sc Dominating Set} problem in random graphs. In a random graph, each pair of vertices are joined by an edge with a probability of $p$, where $p$ is a positive constant less than $1$. We show that, given a…

Data Structures and Algorithms · Computer Science 2015-10-27 Yinglei Song

This paper studies planar drawings of graphs in which each vertex is represented as a point along a sequence of horizontal lines, called levels, and each edge is either a horizontal segment or a strictly $y$-monotone curve. A graph is…

Motivated by applications in graph drawing and information visualization, we examine the planar split thickness of a graph, that is, the smallest $k$ such that the graph is $k$-splittable into a planar graph. A $k$-split operation…

We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…

Data Structures and Algorithms · Computer Science 2025-10-09 Argyrios Deligkas , Eduard Eiben , George Skretas

Obstacle representations of graphs have been investigated quite intensely over the last few years. We focus on graphs that can be represented by a single obstacle. Given a (topologically open) polygon $C$ and a finite set $P$ of points in…

Computational Geometry · Computer Science 2016-09-02 Steven Chaplick , Fabian Lipp , Ji-won Park , Alexander Wolff

In this paper we study the fixed-parameter tractability of the problem of deciding whether a given temporal graph admits a temporal walk that visits all vertices (temporal exploration) or, in some problem variants, a certain subset of the…

Data Structures and Algorithms · Computer Science 2022-12-06 Thomas Erlebach , Jakob T. Spooner

The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph $G$ and a parameter $k$, one has to decide if there is a set $S$ of at most $k$ vertices such that $G-S$ is acyclic. Assuming the…

Data Structures and Algorithms · Computer Science 2026-01-16 Gaétan Berthe , Marin Bougeret , Daniel Gonçalves , Jean-Florent Raymond

The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring the entire network. A power dominating set of a graph is a set of vertices from…

Combinatorics · Mathematics 2017-12-08 Boris Brimkov , Derek Mikesell , Logan Smith

An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the case for the…

Combinatorics · Mathematics 2017-01-02 Florent Foucaud , Guillem Perarnau , Oriol Serra

A graph $G$ is said to be a `set graph' if it admits an acyclic orientation that is also `extensional', in the sense that the out-neighborhoods of its vertices are pairwise distinct. Equivalently, a set graph is the underlying graph of the…

Discrete Mathematics · Computer Science 2015-03-20 Martin Milanič , Romeo Rizzi , Alexandru I. Tomescu

We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence \sigma by at most k vertex or edge deletions…

Data Structures and Algorithms · Computer Science 2016-01-14 Petr A. Golovach , George B. Mertzios

Our goal is to visualize an additional data dimension of a tree with multifaceted data through superimposition on vertical strips, which we call columns. Specifically, we extend upward drawings of unordered rooted trees where vertices have…

Computational Geometry · Computer Science 2023-09-06 Jonathan Klawitter , Johannes Zink

Let $W(G)$ be the Wiener index of a graph $G$. We say that a vertex $v \in V(G)$ is a \v{S}olt\'es vertex in $G$ if $W(G - v) = W(G)$, i.e. the Wiener index does not change if the vertex $v$ is removed. In 1991, \v{S}olt\'es posed the…

Combinatorics · Mathematics 2024-06-05 Nino Bašić , Martin Knor , Riste Škrekovski