Tamara Mchedlidze

Small point sets for simply-nested planar graphs

A point set P⊆ℝ2 is universal for a class

Upward Geometric Graph Embeddings into Point Sets

\cal G

On upward point set embeddability

if every graph of

On ρ-constrained upward topological book embeddings

{\cal G}

Universal Point Sets for Planar Graph Drawings with Circular Arcs

has a planar straight-line embedding into P. We prove that there exists a

Crossing-Optimal Acyclic Hamiltonian Path Completion and Its Application to Upward Topological Book Embeddings

O(n (\frac{\log n}{\log\log n})^2)

Point-Set embeddability of 2-colored trees

size universal point set for the class of simply-nested n-vertex planar graphs. This is a step towards a full answer for the well-known open problem on the size of the smallest universal point sets for planar graphs [1, 5, 9].

Strongly monotone drawings of planar graphs

This volume constitutes the refereed proceedings of the 18th International Symposium on Graph Drawing, GD 2010, held in Konstanz, Germany, during September 2010. The 30 revised full papers presented together with 5 revised short and 8 poster papers were carefully reviewed and selected from 77 submissions. The volume also contains a detailed report about the 17th Annual Graph Drawing Contest, held as a satellite event of GD 2010. Devoted both to theoretical advances as well as to implemented solutions, the papers are concerned with the geometric representation of graphs and networks and are motivated by those applications where it is crucial to visualize structural information as graphs.

Lower and upper bounds for long induced paths in 3-connected planar graphs

We study the problem of upward point set embeddability, that is the problem to decide whether an n-vertex directed graph has an upward planar drawing when its vertices have to be placed on the points of a given point set of size n. We first present some positive and negative results concerning directed trees and convex point sets. Next, we prove that upward point set embeddability can be solved in polynomial time for the case of a directed tree and a convex point set. Further, we extend our approach to the class of outerplanar directed graphs. This implies that upward point set embeddability can be efficiently solved for the case of convex point sets. Finally, we show that the general problem of upward point set embeddability is NP-complete even for 2-convex point sets.

Drawing graphs with vertices at specified positions and crossings at large angles

Giordano, Liotta and Whitesides [1] developed an algorithm that, given an embedded planar st-digraph and a topological numbering ρ of its vertices, computes in O(n2) time a ρ-constrained upward topological book embedding with at most 2n–4 spine crossings per edge. The number of spine crossings per edge is asymptotically worst case optimal.