## Abstract Some of the early questions concerning the maximum genus of a graph have now been answered. In this paper we survey the progress made on such problems and present some recent results, outlining proofs for some of the major theorems.
Results of the maximum genus of graphs
β Scribed by Guang-hua Dong; Yan-pei Liu
- Book ID
- 107347568
- Publisher
- SP Science China Press
- Year
- 2007
- Tongue
- English
- Weight
- 197 KB
- Volume
- 50
- Category
- Article
- ISSN
- 1674-7283
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π SIMILAR VOLUMES
The maximum genus of all vertex-transitive graphs is computed. It is proved that a k-valent vertex-transitive graph of girth g is upper-embeddable whenever k 3 4 or g 2 4. Non-upper-embeddable vertex-transitive graphs are characterized. A particular attention is paid to Cayley graphs. Groups for wh
In this paper, a lower bound on the maximum genus of a graph in terms of its girth is established as follows: let G be a simple graph with minimum degree at least three, and let g be the girth of G. Then ?M(G)~> ~fl(G) + 1 except for G=K4, g-1 where ]~(G) denotes the cycle rank of G and K4 is the co