
On FanCrossing Graphs
A fan is a set of edges with a single common endpoint. A graph is fancr...
read it

Bounding the number of edges of matchstick graphs
We show that a matchstick graph with n vertices has no more than 3nc√(n...
read it

Universal Geometric Graphs
We introduce and study the problem of constructing geometric graphs that...
read it

Graph Planarity Testing with Hierarchical Embedding Constraints
Hierarchical embedding constraints define a set of allowed cyclic orders...
read it

Shortcut Hulls: Vertexrestricted Outer Simplifications of Polygons
Let P be a crossingfree polygon and 𝒞 a set of shortcuts, where each sh...
read it

Approximating the clustered selectedinternal Steiner tree problem
Given a complete graph G=(V,E), with nonnegative edge costs, two subsets...
read it

A linear algorithm for Brick Wang tiling
The Wang tiling is a classical problem in combinatorics. A major theoret...
read it
Synchronized Planarity with Applications to Constrained Planarity Problems
We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loopfree multigraph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges. Synchronized Planarity then asks whether the graph admits a crossingfree embedding into the plane such that the orders of edges around synchronized vertices are consistent. We show, on the one hand, that Synchronized Planarity can be solved in quadratic time, and, on the other hand, that it serves as a powerful modeling language that lets us easily formulate several constrained planarity problems as instances of Synchronized Planarity. In particular, this lets us solve Clustered Planarity in quadratic time, where the most efficient previously known algorithm has an upper bound of O(n^16).
READ FULL TEXT
Comments
There are no comments yet.