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.
Chordal embeddings of planar graphs
✍ Scribed by V. Bouchitté; F. Mazoit; I. Todinca
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 361 KB
- Volume
- 273
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
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.
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