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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
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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
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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
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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
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Synchronized Planarity with Applications to Constrained Planarity Problems [PDF]
, 2021 We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges ...
Fink, Simon D. +2 more
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C-planarity testing of embedded clustered graphs with bounded dual carving-width [PDF]
, 2019 For a clustered graph, i.e, a graph whose vertex set is recursively partitioned into clusters, the C-Planarity Testing problem asks whether it is possible to find a planar embedding of the graph and a representation of each cluster as a region ...
Goodrich Michael +3 more
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Two Simple and Reliable Metrics of Molecular Planarity: Molecular Planarity Parameter (MPP) and Span of Deviation from Plane (SDP) [PDF]
, 2021 Planarity is a very important structural character of molecules, which is closely related to many molecular properties. However, there is currently no simple, universal, and robust way to measure molecular planarity. In order to fill this evident gap, we
Tian, Lu
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Synchronized Planarity with Applications to Constrained Planarity Problems [PDF]
, 2020 We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges ...
Fink, Simon D. +2 more
core +1 more source
On the Complexity of Clustered-Level Planarity and T-Level Planarity
CoRR, 2014 In this paper we study two problems related to the drawing of level graphs, that is, T-LEVEL PLANARITY and CLUSTERED-LEVEL PLANARITY. We show that both problems are NP-complete in the general case and that they become polynomial-time solvable when restricted to proper instances.
Patrizio Angelini +4 more
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, 2004 We provide upper and lower bounds on the least-perimeter way to enclose and separate n regions of equal area in the plane. Along the way, inside the hexagonal honeycomb, we provide minimizers for each n .
Heppes, Aladar, Morgan, Frank
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