One-adhesive polymatroids

04/16/2019

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by   Laszlo Csirmaz, et al.

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Adhesive polymatroids were defined by F. Matúš 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.