on self-approaching and increasing-chord drawings of 3-connected planar graphs
Article Quality & Performance Metrics
Readership in this journal
SteadyRanked #13 of 19 articles by views in canadian journal of infectious diseases and medical microbiology
Bar heights use a square-root scale.
Mint this article as an NFT
Not yet mintedCreate a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.
Abstract
An $st$-path in a drawing of a graph is self-approaching if during the traversal of the corresponding curve from $s$ to any point $t'$ on the curve the distance to $t'$ is non-increasing. A path has increasing chords if it is self-approaching in both directions. A drawing is self-approaching (increasing-chord) if any pair of vertices is connected by a self-approaching (increasing-chord) path.
We study self-approaching and increasing-chord drawings of triangulations and 3-connected planar graphs. We show that in the Euclidean plane, triangulations admit increasing-chord drawings, and for planar 3-trees we can ensure planarity. We prove that strongly monotone (and thus increasing-chord) drawings of trees and binary cactuses require exponential resolution in the worst case, answering an open question by Kindermann et al. (GD 2014). Moreover, we provide a binary cactus that does not admit a self-approaching drawing. Finally, we show that 3-connected planar graphs admit increasing-chord drawings in the hyperbolic plane and characterize the trees that admit such drawings.
| Reference Key |
nllenburg2016journalon
Use this key to autocite in the manuscript while using
SciMatic Manuscript Manager or Thesis Manager
|
|---|---|
| Authors | ;Martin Nöllenburg;Roman Prutkin;Ignaz Rutter |
| Journal | canadian journal of infectious diseases and medical microbiology |
| Year | 2016 |
| DOI |
10.20382/jocg.v7i1a3
|
| URL | |
| Keywords |
Citations
No citations found. To add a citation, contact the admin at info@scimatic.org
Comments
No comments yet. Be the first to comment on this article.