A class of inequalities relating degrees of adjacent nodes to the average degree in edge-weighted uniform hypergraphs
In 1986, Johnson and Perry proved a class of inequalities for uniform hypergraphs which included the following: for any such hypergraph, the geometric mean over the hyperedges of the geometric means of the degrees of the nodes on the hyperedge is no less than the average degree in the hypergraph, wi...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3419 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In 1986, Johnson and Perry proved a class of inequalities for
uniform hypergraphs which included the following: for any such
hypergraph, the geometric mean over the hyperedges of the
geometric means of the degrees of the nodes on the hyperedge is
no less than the average degree in the hypergraph, with equality
only if the hypergraph is regular. Here, we prove a wider class of
inequalities in a wider context, that of edge-weighted uniform
hypergraphs. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |