Related papers: Linear Arrangement of Halin Graphs
Traditionally, the quality of orthogonal planar drawings is quantified by either the total number of bends, or the maximum number of bends per edge. However, this neglects that in typical applications, edges have varying importance.…
An {\em ordered $r$-graph} is an $r$-uniform hypergraph whose vertex set is linearly ordered. Given $2\leq k\leq r$, an ordered $r$-graph $H$ is {\em interval} $k$-{\em partite} if there exist at least $k$ disjoint intervals in the ordering…
We analyze the performance of a class of manifold-learning algorithms that find their output by minimizing a quadratic form under some normalization constraints. This class consists of Locally Linear Embedding (LLE), Laplacian Eigenmap,…
A (vertex) $\ell$-ranking is a colouring $\varphi:V(G)\to\mathbb{N}$ of the vertices of a graph $G$ with integer colours so that for any path $u_0,\ldots,u_p$ of length at most $\ell$, $\varphi(u_0)\neq\varphi(u_p)$ or…
An arrangement of circles in which circles intersect only in angles of $\pi/2$ is called an \emph{arrangement of orthogonal circles}. We show that in the case that no two circles are nested, the intersection graph of such an arrangement is…
The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no…
A planar orthogonal drawing $\Gamma$ of a planar graph $G$ is a geometric representation of $G$ such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and no two…
The girth of a graph is the minimum weight of all simple cycles of the graph. We study the problem of determining the girth of an n-node unweighted undirected planar graph. The first non-trivial algorithm for the problem, given by Djidjev,…
An ordered graph is a pair $\mathcal{G}=(G,\prec)$ where $G$ is a graph and $\prec$ is a total ordering of its vertices. The ordered Ramsey number $\overline{R}(\mathcal{G})$ is the minimum number $N$ such that every $2$-coloring of the…
A simple digraph is semi-complete if for any two of its vertices $u$ and $v$, at least one of the arcs $(u,v)$ and $(v,u)$ is present. We study the complexity of computing two layout parameters of semi-complete digraphs: cutwidth and…
Network Diversion is a graph problem that has been extensively studied in both the network-analysis and operations-research communities as a measure of how robust a network is against adversarial disruption. This problem is especially well…
Given a graph of which the n vertices form a regular two-dimensional grid, and in which each (possibly weighted and/or directed) edge connects a vertex to one of its eight neighbours, the following can be done in O(scan(n)) I/Os, provided M…
We propose a new arrangement problem on directed graphs, Maximum Directed Linear Arrangement (MaxDLA). This is a directed variant of a similar problem for undirected graphs, in which however one seeks maximum and not minimum; this problem…
Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set;…
Network topology matrices are algebraic representations of graphs that are widely used in modeling and analysis of various applications including electrical circuits, communication networks and transportation systems. In this paper, we…
We study the Minimum Crossing Number problem: given an $n$-vertex graph $G$, the goal is to find a drawing of $G$ in the plane with minimum number of edge crossings. This is one of the central problems in topological graph theory, that has…
A track layout of a graph consists of a vertex coloring and a total order of each color class, such that no two edges cross between any two color classes. The track number of a graph is the minimum number of colors required by a track…
We present space-efficient algorithms for computing cut vertices in a given graph with $n$ vertices and $m$ edges in linear time using $O(n+\min\{m,n\log \log n\})$ bits. With the same time and using $O(n+m)$ bits, we can compute the…
A planar orthogonal drawing of a planar 4-graph G (i.e., a planar graph with vertex-degree at most four) is a crossing-free drawing that maps each vertex of G to a distinct point of the plane and each edge of $G$ to a sequence of horizontal…
This paper studies optimal-area visibility representations of $n$-vertex outer-1-plane graphs, i.e. graphs with a given embedding where all vertices are on the boundary of the outer face and each edge is crossed at most once. We show that…