Open AccessPosted Content
2-connecting Outerplanar Graphs without Blowing Up the Pathwidth
Reads0
Chats0
TLDR
In this article, the problem of computing minimum height planar straight line drawings of outerplanar graphs with their vertices placed on a two-dimensional grid was solved for 2-vertex-connected graphs.Abstract:
Given a connected outerplanar graph G of pathwidth p, we give an algorithm to add edges to G to get a supergraph of G, which is 2-vertex-connected, outerplanar and of pathwidth O(p). This settles an open problem raised by Biedl, in the context of computing minimum height planar straight line drawings of outerplanar graphs, with their vertices placed on a two dimensional grid. In conjunction with the result of this paper, the constant factor approximation algorithm for this problem obtained by Biedl for 2-vertex-connected outerplanar graphs will work for all outer planar graphs.read more
Citations
More filters
Journal ArticleDOI
A polynomial-time algorithm for Outerplanar Diameter Improvement
Nathann Cohen,Daniel Gonçalves,Eun Jung Kim,Christophe Paul,Ignasi Sau,Dimitrios M. Thilikos,Dimitrios M. Thilikos,Dimitrios M. Thilikos,Mathias Weller +8 more
TL;DR: In this article, a dynamic programming algorithm was proposed to solve the outerplanar diameter improvement problem in polynomial time, where the problem is to add edges to a graph G in such a way that the resulting graph is planar and has diameter at most D.
Book ChapterDOI
2-connecting Outerplanar Graphs without Blowing Up the Pathwidth
TL;DR: An algorithm is given to add edges to G to get a supergraph of G, which is 2-vertex-connected, outerplanar and of pathwidth O(p), which settles an open problem raised by Biedl.
Book ChapterDOI
A Polynomial-Time Algorithm for Outerplanar Diameter Improvement
Nathann Cohen,Daniel Gonçalves,Eun Jung Kim,Christophe Paul,Ignasi Sau,Dimitrios M. Thilikos,Dimitrios M. Thilikos,Dimitrios M. Thilikos,Mathias Weller +8 more
TL;DR: A dynamic programming algorithm is provided that solves the Outerplanar Diameter Improvement problem in polynomial time and demonstrates several structural analogues to the celebrated and challenging Planar D diameter Improvement problem, where the resulting graph should, instead, be planar.
Posted Content
Transforming planar graph drawings while maintaining height.
TL;DR: It is shown that many of planar graph drawings can be transformed from one style to another without changing the height of the drawing.
Book ChapterDOI
On the Treewidth of Planar Minor Free Graphs
Youssou Dieng,Cyril Gavoille +1 more
TL;DR: It is proved that the treewidth of every planar graph excluding a graph having a poly-line \(p \times q\)-grid drawing is \(O(p\sqrt{q})", which is asymptotically optimal.
References
More filters
Journal ArticleDOI
Algorithm 447: efficient algorithms for graph manipulation
TL;DR: Efficient algorithms are presented for partitioning a graph into connected components, biconnected components and simple paths and each iteration produces a new path between two vertices already on paths.
Journal ArticleDOI
Graph minors. III. Planar tree-width
Neil Robertson,Paul Seymour +1 more
TL;DR: It is proved that for any fixed planar graph H, every planar graphs with sufficiently large tree-width has a minor isomorphic to H.
Proceedings ArticleDOI
Embedding planar graphs on the grid
TL;DR: It is shown that each plane graph of order n 2 3 has a straight line embedding on the n-2 by n-1 grid that is computable in time O(n), and a nice feature of the vertex-coordinates is that they have a purely combinatorial meaning.
Journal ArticleDOI
Regular ArticleGraph Minors: XV. Giant Steps
Neil Robertson,Paul Seymour +1 more
TL;DR: In this paper, the authors studied the problem of drawing a graph with a subgraph with high representativity on a surface and showing that the drawing of the subgraph can be extended up to 3-separations if a bounded number of "vortices" are present in the drawing.
Journal Article
Planar Permutation Graphs
Gary Chartrand,Frank Harary +1 more
TL;DR: Gauthier-Villars as mentioned in this paper implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).