Related papers: Pseudoline arrangement graphs: degree sequences an…
The degree distribution is one of the most fundamental properties used in the analysis of massive graphs. There is a large literature on graph sampling, where the goal is to estimate properties (especially the degree distribution) of a…
We study the combinatorics of pseudoline arrangements in the real projective plane. Our focus lies on two classes of arrangements: simplicial arrangements and arrangements whose characteristic polynomials have only real roots. We derive…
Line graphs are an alternative representation of graphs where each vertex of the original (root) graph becomes an edge. However not all graphs have a corresponding root graph, hence the transformation from graphs to line graphs is not…
We investigate several topological and combinatorial properties of line arrangements. We associate to a line arrangement a link obtained by intersecting the arrangement with some sphere. Several topics are discussed: (a) some link…
Let $G$ be a graph that is topologically embedded in the plane and let $\mathcal{A}$ be an arrangement of pseudolines intersecting the drawing of $G$. An aligned drawing of $G$ and $\mathcal{A}$ is a planar polyline drawing $\Gamma$ of $G$…
A visibility representation is a classical drawing style of planar graphs. It displays the vertices of a graph as horizontal vertex-segments, and each edge is represented by a vertical edge-segment touching the segments of its end vertices;…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We study the problem of embedding graphs in the plane as good geometric spanners. That is, for a graph $G$, the goal is to construct a straight-line drawing $\Gamma$ of $G$ in the plane such that, for any two vertices $u$ and $v$ of $G$,…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
We suggest two related conjectures dealing with the existence of spanning irregular subgraphs of graphs. The first asserts that any $d$-regular graph on $n$ vertices contains a spanning subgraph in which the number of vertices of each…
We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time…
We characterize the graphs with loops whose degree sequences have no repeated values and find their adjacency spectrum. In the case of simple graphs, such graphs are called anti-regular graphs and are examples of threshold graphs. The…
Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs…
A sum graph is a finite simple graph whose vertex set is labeled with distinct positive integers such that two vertices are adjacent if and only if the sum of their labels is itself another label. The spum of a graph $G$ is the minimum…
The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
We systematically study a natural problem in extremal graph theory, to minimize the number of edges in a graph with a fixed number of vertices, subject to a certain local condition: each vertex must be in a copy of a fixed graph $H$. We…
We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline…