Related papers: Experimental Evaluation of Book Drawing Algorithms
A $k$-stack layout (or $k$-page book embedding) of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing edges with respect to the vertex order. The stack number of a graph is the…
A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge. The study of 1-planar graphs dates back…
A $k$-truss is an edge-induced subgraph $H$ such that each of its edges belongs to at least $k-2$ triangles of $H$. This notion has been introduced around ten years ago in social network analysis and security, as a form of cohesive subgraph…
A simple graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ iff $xy\in E$. Word-representable graphs generalize several important classes of graphs. A graph…
In this paper, we introduce the following new concept in graph drawing. Our task is to find a small collection of drawings such that they all together satisfy some property that is useful for graph visualization. We propose investigating a…
We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for {\em graphs with semi-edges}. The notion of graph covering is a discretization of coverings between surfaces or topological…
Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in…
In this work we investigate the complexity of some problems related to the {\em Simultaneous Embedding with Fixed Edges} (SEFE) of $k$ planar graphs and the PARTITIONED $k$-PAGE BOOK EMBEDDING (PBE-$k$) problems, which are known to be…
The online dominating set problem is an online variant of the minimum dominating set problem, which is one of the most important NP-hard problems on graphs. This problem is defined as follows: Given an undirected graph $G = (V, E)$, in…
Let $G$ be a complete edge-weighted graph on $n$ vertices. To each subset of vertices of $G$ assign the cost of the minimum spanning tree of the subset as its weight. Suppose that $n$ is a multiple of some fixed positive integer $k$. The…
Recent cognitive experiments have shown that the negative impact of an edge crossing on the human understanding of a graph drawing, tends to be eliminated in the case where the crossing angles are greater than 70 degrees. This motivated the…
Recently, a new way of avoiding crossings in straight-line drawings of non-planar graphs has been investigated. The idea of partial edge drawings (PED) is to drop the middle part of edges and rely on the remaining edge parts called stubs.…
A linear layout of a graph consists of a linear ordering of its vertices and a partition of its edges into pages such that the edges assigned to the same page obey some constraint. The two most prominent and widely studied types of linear…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…
In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices, and reports every vertex and edge exactly once. To achieve this, we combine a given geometric graph $G$ with the integer lattice, seen as a…
Graph labellings have been a very fruitful area of research in the last four decades. However, despite the staggering number of papers published in the field (over 1000), few general results are available, and most papers deal with…
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…