Packings and coverings in graphs

Packings and coverings in graphs are related to two main problems of

graph theory, respectively error correcting codes and domination.

Given a set of words, an error correcting code is a subset such that

any two words in the subset are rather far apart, and can be

identified even if some errors occured during transmission. Error

correcting codes have been well studied already, and a famous example

of perfect error correcting codes are Hamming codes.

Domination is also a very old problem, initiated by some Chess problem

in the 1860's, yet Berge proposed the corresponding problem on graphs

only in the 1960's. In a graph, a subset of vertices dominates all the

graph if every vertex of the graph is neighbour of a vertex of the

subset. The domination number of a graph is the minimum number of

vertices in a dominating set. Many variants of domination have been

proposed since, leading to a very large literature.

During this talk, we will see how these two problems are related and

get into few results on these topics.