Michael A. Bekos
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View article: Drawing graphs with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si21.svg"> <mml:mi>k</mml:mi> </mml:math> vertices per face: Complexity and algorithms
Drawing graphs with vertices per face: Complexity and algorithms Open
View article: On k-planar Graphs without Short Cycles
On k-planar Graphs without Short Cycles Open
We study the impact of forbidding short cycles to the edge density of k-planar graphs; a k-planar graph is one that can be drawn in the plane with at most k crossings per edge. Specifically, we consider three settings, according to which t…
View article: Graph Product Structure for $h$-Framed Graphs
Graph Product Structure for $h$-Framed Graphs Open
Graph product structure theory expresses certain graphs as subgraphs of the strong product of much simpler graphs. In particular, an elegant formulation for the corresponding structural theorems involves the strong product of a path and of…
View article: Guest Editors' Foreword
Guest Editors' Foreword Open
Special Issue on GD 2023: Guest Editors' Foreword
View article: Weakly Leveled Planarity with Bounded Span
Weakly Leveled Planarity with Bounded Span Open
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 $s$-…
View article: On $k$-planar Graphs without Short Cycles
On $k$-planar Graphs without Short Cycles Open
We study the impact of forbidding short cycles to the edge density of $k$-planar graphs; a $k$-planar graph is one that can be drawn in the plane with at most $k$ crossings per edge. Specifically, we consider three settings, according to w…
View article: Convex grid drawings of planar graphs with constant edge-vertex resolution
Convex grid drawings of planar graphs with constant edge-vertex resolution Open
In this work, we continue the study of the area required for convex straight-line grid drawings of 3-connected plane graphs, which has been intensively investigated in the last decades. Motivated by applications, such as graph editors, we …
View article: Recognizing Map Graphs of Bounded Treewidth
Recognizing Map Graphs of Bounded Treewidth Open
A map is a partition of the sphere into interior-disjoint regions homeomorphic to closed disks. Some regions are labeled as nations, while the remaining ones are labeled as holes. A map in which at most k nations touch at the same point is…
View article: Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023)
Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023) Open
This is the arXiv index for the electronic proceedings of GD 2023, which contains the peer-reviewed and revised accepted papers with an optional appendix. Proceedings (without appendices) are also to be published by Springer in the Lecture…
View article: Book embeddings of k-framed graphs and k-map graphs
Book embeddings of k-framed graphs and k-map graphs Open
View article: On the Deque and Rique Numbers of Complete and Complete Bipartite Graphs
On the Deque and Rique Numbers of Complete and Complete Bipartite Graphs Open
Several types of linear layouts of graphs are obtained by leveraging known data structures; the most notable representatives are the stack and the queue layouts. In this content, given a data structure, one seeks to specify an order of the…
View article: Bitonic st-Orderings for Upward Planar Graphs: Splits and Bends in the Variable Embedding Scenario
Bitonic st-Orderings for Upward Planar Graphs: Splits and Bends in the Variable Embedding Scenario Open
Bitonic st -orderings for st -planar graphs were introduced as a method to cope with several graph drawing problems. Notably, they have been used to obtain the best-known upper bound on the number of bends for upward planar polyline drawin…
View article: Splitting Vertices in 2-Layer Graph Drawings
Splitting Vertices in 2-Layer Graph Drawings Open
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel line…
View article: Recognizing DAGs with page-number 2 is NP-complete
Recognizing DAGs with page-number 2 is NP-complete Open
The page-number of a directed acyclic graph (a DAG, for short) is the minimum k for which the DAG has a topological order and a k-coloring of its edges such that no two edges of the same color cross, i.e., have alternating endpoints along …
View article: Axis-Parallel Right Angle Crossing Graphs
Axis-Parallel Right Angle Crossing Graphs Open
A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominen…
View article: Lazy Queue Layouts of Posets
Lazy Queue Layouts of Posets Open
We investigate the queue number of posets in terms of their width, that is, the maximum number of pairwise incomparable elements. A long-standing conjecture of Heath and Pemmaraju asserts that every poset of width w has queue number at mos…
View article: An Improved Upper Bound on the Queue Number of Planar Graphs
An Improved Upper Bound on the Queue Number of Planar Graphs Open
A k -queue layout is a special type of a linear layout, in which the linear order avoids $$(k+1)$$ -rainbows, that is, $$k+1$$ independent edges that pairwise form a nested pair. The optimization goal is to determine the queue …
View article: The Rique-Number of Graphs
The Rique-Number of Graphs Open
We continue the study of linear layouts of graphs in relation to known data structures. At a high level, given a data structure, the goal is to find a linear order of the vertices of the graph and a partition of its edges into pages, such …
View article: Recognizing DAGs with Page-Number 2 is NP-complete
Recognizing DAGs with Page-Number 2 is NP-complete Open
The page-number of a directed acyclic graph (a DAG, for short) is the minimum $k$ for which the DAG has a topological order and a $k$-coloring of its edges such that no two edges of the same color cross, i.e., have alternating endpoints al…
View article: Strictly-Convex Drawings of $3$-Connected Planar Graphs
Strictly-Convex Drawings of $3$-Connected Planar Graphs Open
Strictly-convex straight-line drawings of $3$-connected planar graphs in small area form a classical research topic in Graph Drawing. Currently, the best-known area bound for such drawings is $O(n^2) \times O(n^2)$, as shown by Bárány and …
View article: RAC Drawings of Graphs with Low Degree
RAC Drawings of Graphs with Low Degree Open
Motivated by cognitive experiments providing evidence that large crossing-angles do not impair the readability of a graph drawing, RAC (Right Angle Crossing) drawings were introduced to address the problem of producing readable representat…
View article: On Turn-Regular Orthogonal Representations
On Turn-Regular Orthogonal Representations Open
An interesting class of orthogonal representations consists of the so-called turn-regular ones, i.e., those that do not contain any pair of reflex corners that ``point to each other'' inside a face. For such a representation $H$ it is poss…
View article: Universal Slope Sets for Upward Planar Drawings
Universal Slope Sets for Upward Planar Drawings Open
We study universal sets of slopes for computing upward planar drawings of planar st -graphs. We first consider a subfamily of planar st -graphs, called bitonic st -graphs. We prove that every set $$\mathcal {S}$$ of $$\varDelta $$ slop…
View article: Convex Grid Drawings of Planar Graphs with Constant Edge-Vertex Resolution
Convex Grid Drawings of Planar Graphs with Constant Edge-Vertex Resolution Open
We continue the study of the area requirement of convex straight-line grid drawings of 3-connected plane graphs, which has been intensively investigated in the last decades. Motivated by applications, such as graph editors, we additionally…
View article: Graph Product Structure for h-Framed Graphs
Graph Product Structure for h-Framed Graphs Open
Graph product structure theory expresses certain graphs as subgraphs of the strong product of much simpler graphs. In particular, an elegant formulation for the corresponding structural theorems involves the strong product of a path and of…
View article: Computing Schematic Layouts for Spatial Hypergraphs on Concentric Circles and Grids
Computing Schematic Layouts for Spatial Hypergraphs on Concentric Circles and Grids Open
Set systems can be visualized in various ways. An important distinction between techniques is whether the elements have a spatial location that is to be used for the visualization; for example, the elements are cities on a map. Strictly ad…
View article: On Mixed Linear Layouts of Series-Parallel Graphs
On Mixed Linear Layouts of Series-Parallel Graphs Open
View article: Recognizing Map Graphs of Bounded Treewidth
Recognizing Map Graphs of Bounded Treewidth Open
A map graph is one admitting a representation in which vertices are nations on a spherical map and edges are shared curve segments or points between nations. We present an explicit fixed-parameter tractable algorithm for recognizing map gr…
View article: The Mixed Page Number of Graphs
The Mixed Page Number of Graphs Open
A linear layout of a graph typically consists of a total vertex order, and a partition of the edges into sets of either non-crossing edges, called stacks, or non-nested edges, called queues. The stack (queue) number of a graph is the minim…
View article: Grid drawings of graphs with constant edge-vertex resolution
Grid drawings of graphs with constant edge-vertex resolution Open