Groupe d’études et de recherche en analyse des décisions

# Using graph theory to derive inequalities for the Bell numbers

## Alain Hertz, Anaelle Hertz et Hadrien Mélot

The Bell numbers count the number of different ways to partition a set of $$n$$ elements while the graphical Bell numbers count the number of non-equivalent partitions of the vertex set of a graph into stable sets. This relation between graph theory and integer sequences has motivated us to study properties on the average number of colors in the non-equivalent colorings of a graph to discover new non trivial inequalities for the Bell numbers. Example are given to illustrate our approach.

, 18 pages