## 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.
On the maximum genus of a graph
β Scribed by E.A Nordhaus; B.M Stewart; A.T White
- Publisher
- Elsevier Science
- Year
- 1971
- Tongue
- English
- Weight
- 415 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
It is proved that every connected simplicial graph with minimum valence at least three has maximum genus at least one-quarter of its cycle rank. This follows from the technical result that every 3-regular simplicial graph except K4 has a Xuong co-tree whose odd components have only one edge each. It
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
Abstrart. The maximum genus of a connected graph (: is the maximum among the genera of a!1 cornpact olientable 2-manifolds upon which G has 2-&l embeddings. In the theorems that fc-llow the use of an edg;:-adding techniq se is combined with ihe well-known Edmonds' technique to prfiruce the desired r