  Adhesive polymatroids were defined by F. Mat\'u\v{s} motivated by entropy
functions. Two polymatroids are adhesive if they can be glued together along
their joint part in a modular way; and are one-adhesive, if one of them has a
single point outside their intersection. It is shown that two polymatroids are
one-adhesive if and only if two closely related polymatroids have any
extension. Using this result, adhesive polymatroid pairs on a five-element set
are characterized.
