Re-embeddings of Maximum 1-Planar Graphs
β Scribed by Suzuki, Yusuke
- Book ID
- 115490726
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2010
- Tongue
- English
- Weight
- 300 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0895-4801
No coin nor oath required. For personal study only.
π 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 identify the structures of 4-connected projective-planar graphs which generate their inequivalent embeddings on the projective plane, showing two series of graphs the number of whose inequivalent embeddings is held by O(n) with respect to the number of its vertices n.
It will be shown that the number of equivalence classes of embeddings of a 3-connected nonplanar graph into a projective plane coincides with the number of isomorphism classes of planar double coverings of the graph and a combinatorial method to determine the number will be developed.