Column planarity and partially-simultaneous geometric embedding

Planarity Testing and Embedding

Universita’ di Roma Tre 3.1 Properties and Characterizations of Planar Graphs . . . . . 2 Basic Definitions • Properties • Characterizations 3.2 Planarity Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3 History of Planarity Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.4 Common Algorithmic Techniques and Tools . . . . . ...

Planar and Quasi Planar Simultaneous Geometric Embedding

Track Planarity Testing and Embedding

A track graph is a graph with its vertex set partitioned into horizontal levels. It is track planar if there are permutations of the vertices on each level such that all edges can be drawn as weak monotone curves without crossings. The novelty and generalisation over level planar graphs is that horizontal edges connecting consecutive vertices on the same level are allowed. We show that track pl...

The Complexity of Simultaneous Geometric Graph Embedding

Given a collection of planar graphs G1, . . . , Gk on the same set V of n vertices, the simultaneous geometric embedding (with mapping) problem, or simply k-SGE, is to find a set P of n points in the plane and a bijection φ : V → P such that the induced straight-line drawings of G1, . . . , Gk under φ are all plane. This problem is polynomial-time equivalent to weak rectilinear realizability of...

Simultaneous Orthogonal Planarity

We introduce and study the OrthoSEFE-k problem: Given k planar graphs each with maximum degree 4 and the same vertex set, do they admit an OrthoSEFE, that is, is there an assignment of the vertices to grid points and of the edges to paths on the grid such that the same edges in distinct graphs are assigned the same path and such that the assignment induces a planar orthogonal drawing of each of...