A 0-1 matrix A is ideal if the polyhedron Q(A) = conv{x is an element
of Q(V): A . x greater than or equal to 1, x greater than or equal to
0} (V denotes the column index set of A) is integral. Similarly a matr
ix is perfect if P(A) = conv{x is an element of Q(V): A . x less than
or equal to 1, x greater than or equal to 0} is integral. Little is kn
own about the relationship between these two classes of matrices. We c
onsider a transformation between the two classes which enables us to a
pply Lehman's modified theorem about deletion-minimal nonideal matrice
s to obtain new results about packing polyhedra. This results in a pol
yhedral description for the stable set polytopes of near-bipartite gra
phs (the deletion of any neighbourhood produces a bipartite graph). No
te that this class includes the complements of line graphs. To date, t
his is the only natural class, besides the perfect graphs, for which s
uch a description is known for the graphs and their complements. Some
remarks are also made on possible approaches to describing the stable
set polyhedra of quasi-line graphs, and more generally claw-free graph
s. These results also yield a new class of t-perfect graphs.