We prove that every planar graph on \(n\) vertices is contained in a chordal graph with at most \(c n \log n\) edges for some abolsute constant \(c\) and this is best possible to within a constant factor. 1994 Academic Press, Inc.
Equilateral Drawing of 2-Connected Planar Chordal Graphs
✍ Scribed by L. Markenzon; N. Paciornik
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 255 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Robertson and Seymour conjectured that the treewidth of a planar graph and the treewidth of its geometric dual di er by at most one. Lapoire solved the conjecture in the a rmative, using algebraic techniques. We give here a much shorter proof of this result.
We prove that every planar 3-connected graph has a 2-connected spanning subgraph of maximum valence 15 . We give an example of a planar 3 -connected graph with no spanning 2-connected subgraph of maximum valence five. i) 1994 Academic Press, Inc.
## Abstract Let __G__ be a graph drawn in the plane so that its edges are represented by __x__‐monotone curves, any pair of which cross an even number of times. We show that __G__ can be redrawn in such a way that the __x__‐coordinates of the vertices remain unchanged and the edges become non‐cross
## Abstract Suppose __G = (V, E)__ is a graph in which every vertex __x__ has a non‐negative real number __w(x)__ as its weight. The __w__‐distance sum of a vertex __y__ is __D~G, w~(y)__ = σ~x≅v~ __d(y, x)w(x).__ The __w__‐median of __G__ is the set of all vertices __y__ with minimum __w__‐distanc