Related papers: Rectilinear Planarity of Partial 2-Trees
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…
In this paper, we study the area requirements of planar straight-line orthogonal drawings of ternary trees. We prove that every ternary tree admits such a drawing in sub-quadratic area. Further, we present upper bounds, the outcomes of an…
In this paper, we study the outerplanarity of planar graphs, i.e., the number of times that we must (in a planar embedding that we can initially freely choose) remove the outerface vertices until the graph is empty. It is well-known that…
The geometric bottleneck Steiner network problem on a set of vertices $X$ embedded in a normed plane requires one to construct a graph $G$ spanning $X$ and a variable set of $k\geq 0$ additional points, such that the length of the longest…
This paper studies the problem of computing quasi-upward planar drawings of bimodal plane digraphs with minimum curve complexity, i.e., drawings such that the maximum number of bends per edge is minimized. We prove that every bimodal plane…
The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…
Consider the following problem: Given a planar graph $G$, what is the maximum number $p$ such that $G$ has a planar straight-line drawing with $p$ collinear vertices? This problem resides at the core of several graph drawing problems,…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…
We first prove a one-to-one correspondence between finding Hamiltonian cycles in a cubic planar graphs and finding trees with specific properties in dual graphs. Using this information, we construct an exact algorithm for finding…
Given a planar graph $G$ and a partition of the neighbors of each vertex $v$ in four sets $UR(v)$, $UL(v)$, $DL(v)$, and $DR(v)$, the problem Windrose Planarity asks to decide whether $G$ admits a windrose-planar drawing, that is, a planar…
The problem of extending partial geometric graph representations such as plane graphs has received considerable attention in recent years. In particular, given a graph $G$, a connected subgraph $H$ of $G$ and a drawing $\mathcal{H}$ of $H$,…
We introduce and study the problem \mpd, which asks for two planar graphs $G_1$ and $G_2$ whether $G_1$ can be embedded such that its dual is isomorphic to $G_2$. Our algorithmic main result is an NP-completeness proof for the general case…
We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
We introduce and study the problem Ordered Level Planarity which asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a y-monotone curve. This can be…
There has recently been much progress on exact algorithms for the (un)weighted graph (bi)partitioning problem using branch-and-bound and related methods. In this note we present and improve an easily computable, purely combinatorial lower…
There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…
We show that the eccentricities, diameter, radius, and Wiener index of an undirected $n$-vertex graph with nonnegative edge lengths can be computed in time $O(n\cdot \binom{k+\lceil\log n\rceil}{k} \cdot 2^k k^2 \log n)$, where $k$ is the…
Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…