Results 11 to 20 of about 844 (217)
Overlapping cluster planarity [PDF]
2007 6th International Asia-Pacific Symposium on Visualization, 2007 Summary: This paper investigates a new direction in the area of cluster planarity by addressing the following question: Let G be a graph along with a hierarchy of vertex clusters, where clusters can partially intersect. Does G admit a drawing where each cluster is inside a simple closed region, no two edges intersect, and no edge intersects a region ...
DIDIMO, WALTER +2 more
openaire +3 more sources
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2021 Discontinuity sets play an essential and pivotal role in the deformation monitoring and stability analysis of the rock mass, but there are still many challenges for accurately and rapidly extracting discontinuity.
Wenxiao Sun +3 more
doaj +1 more source
Clustered Planarity Testing Revisited [PDF]
The Electronic Journal of Combinatorics, 2014 The Hanani–Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generalize this result to clustered graphs with two disjoint clusters, and show that a straightforward ...
Radoslav Fulek +3 more
openaire +5 more sources
Atomic Embeddability, Clustered Planarity, and Thickenability [PDF]
Journal of the ACM, 2020 We study the atomic embeddability testing problem, which is a common generalization of clustered planarity ( c-planarity , for short) and thickenability testing, and present a polynomial-time algorithm for this problem, thereby giving the first polynomial-time algorithm for c-planarity.
Radoslav Fulek, Csaba D. Tóth
openaire +3 more sources
A Note on Obstructions to Clustered Planarity [PDF]
The Electronic Journal of Combinatorics, 2011 A planar digraph $D$ is clustered planar if in some planar embedding of $D$ we have at each vertex the in-arcs occurring sequentially in the local rotation. By supplementing the operations used to form the usual minors in Kuratowski's theorem, clustered planar digraphs are characterised.
Sneddon, Jamie, Bonnington, Paul
openaire +3 more sources
Planarity-Preserving Clustering and Embedding for Large Planar Graphs [PDF]
Computational Geometry, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christian A. Duncan +2 more
openaire +2 more sources
Toward a Theory of Planarity: Hanani-Tutte and Planarity Variants
Journal of Graph Algorithms and Applications, 2013 We study Hanani-Tutte style theorems for various notions of planarity, including partially embedded planarity and simultaneous planarity. This approach brings together the combinatorial, computational and algebraic aspects of planarity notions and may ...
Marcus Schaefer
doaj +1 more source
Planarization of Clustered Graphs [PDF]
, 2002 We propose a planarization algorithm for clustered graphs and experimentally test its efficiency and effectiveness. Further, we integrate our planarization strategy into a complete topology-shape-metrics algorithm for drawing clustered graphs in the orthogonal drawing convention.
Di Battista G. +2 more
openaire +2 more sources
Intersection-Link Representations of Graphs
Journal of Graph Algorithms and Applications, 2017 We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex $u$ is represented by a geometric object $R(u)$ and each edge $(u,v)$ is represented by the intersection ...
Patrizio Angelini +5 more
doaj +1 more source
Efficient C-Planarity Testing for Embedded Flat Clustered Graphs with Small Faces
Journal of Graph Algorithms and Applications, 2009 Let C be a clustered graph and suppose that the planar embedding of its underlying graph is fixed. Is testing the c-planarity of C easier than in the variable embedding setting?
Giuseppe Di Battista, Fabrizio Frati
doaj +1 more source