Results 31 to 40 of about 1,484,168 (305)
Discrete Applied Mathematics, 2017 A graph is NIC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share at most one common end vertex. NIC-planarity generalizes IC-planarity, which allows a vertex to be incident to at most one crossing edge, and specializes 1-planarity, which only requires at most one crossing per ...
Christian Bachmaier +4 more
openaire +3 more sources
Box-Rectangular Drawings of Planar Graphs
Journal of Graph Algorithms and Applications, 2013 A plane graph is a planar graph with a fixed planar embedding in the plane. In a box- rectangular drawing of a plane graph, every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal line segment or a vertical line ...
Md. Manzurul Hasan +2 more
doaj +1 more source
Planar L-Drawings of Bimodal Graphs
Journal of Graph Algorithms and Applications, 2022 In a planar L-drawing of a directed graph (digraph) each edge $e$ is represented as a polyline composed of a vertical segment starting at the tail of $e$ and a horizontal segment ending at the head of $e$. Distinct edges may overlap, but not cross.
Patrizio Angelini +3 more
doaj +1 more source
Connectivity of Planar Graphs [PDF]
Journal of Graph Algorithms and Applications, 2001 We give here three simple linear time algorithms on planar graphs: a 4-connexity test for maximal planar graphs, an algorithm enumerating the triangles and a 3-connexity test. Although all these problems got already linear-time solutions, the presented algorithms are both simple and efficient. They are based on some new theoretical results.
de Fraysseix, Hubert +1 more
openaire +3 more sources
On a Class of Planar Graphs with Straight-Line Grid Drawings on Linear Area
Journal of Graph Algorithms and Applications, 2009 A straight-line grid drawing of a planar graph G is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings.
Md. Rezaul Karim, Md. Saidur Rahman
doaj +1 more source
Drawing Partially Embedded and Simultaneously Planar Graphs
Journal of Graph Algorithms and Applications, 2015 We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem-to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph-and the simultaneous ...
Timothy Chan +5 more
doaj +1 more source
Fitting Planar Graphs on Planar Maps [PDF]
Journal of Graph Algorithms and Applications, 2014 Graph and cartographic visualization have the common objective to provide intuitive understanding of some underlying data. We consider a problem that combines aspects of both by studying the problem of fitting planar graphs on planar maps. After providing an NP-hardness result for the general decision problem, we identify sufficient conditions so ...
Md. Jawaherul Alam +3 more
openaire +2 more sources
Planar Octilinear Drawings with One Bend Per Edge
Journal of Graph Algorithms and Applications, 2015 In octilinear drawings of planar graphs, every edge is drawn as a sequence of horizontal, vertical and diagonal (45°) line segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few bends per edge.
Michael Bekos +3 more
doaj +1 more source
Recurrence of planar graph limits [PDF]
, 2012 We prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform infinite planar triangulation and quadrangulation (UIPT and UIPQ)
O. Gurel-Gurevich, Asaf Nachmias
semanticscholar +1 more source
On Longest Cycles in Essentially 4-Connected Planar Graphs
Discussiones Mathematicae Graph Theory, 2016 A planar 3-connected graph G is essentially 4-connected if, for any 3-separator S of G, one component of the graph obtained from G by removing S is a single vertex.
Fabrici Igor +2 more
doaj +1 more source