Two lower bounds are obtained for the average genus of graphs. The average genus for a graph of maximum valence at most 3 is at least half its maximum genus, and the average genus for a 2-connected simplicial graph other than a cycle is at least 1/16 of its cycle rank.
Bounds for the Genus of Space Curves
โ Scribed by Valentina Beorchia
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 537 KB
- Volume
- 184
- Category
- Article
- ISSN
- 0025-584X
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โฆ Synopsis
Abstract
We compute the following upper bounds for the maximal arithmetic genus P~a~(d,t) over all locally Cohen โ Macaulay space curves of degree d, which are not contained in a surface of degree magnified image These bounds are sharp for t โค 4 abd any d โฅ t.
๐ SIMILAR VOLUMES
This paper is devoted to extend some well-known facts on the genus of a surface and on the Heegaard genus of a 3-manifold to manifolds of arbitrary dimension. More precisely, we prove that the genus of non-orientable manifolds is always even and we compare the genus of a manifold with the rank of it
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