In this section we survey the results known about the compactness of
graphs, that is the smallest integer k that provides a shortest path
k-IRS. We start with some general results. Recall that the
compactness of G is denoted by
,
(
and
)
denotes the linear compactness (
strict and strict-linear compactness). See Paragraph 2.5.
For convenience, for every class of graphs ,
we denote by
the value defined by: