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This would imply the following conjecture of Frank:
'''Conjecture.''' If ''P'' is an integer 2-polymatroid which contains the '''1''' (all-ones) vector, then it has a vertex ''v'' such that '''12'''-''v'' is in ''P''.
It is known by the [[Matroid union theorem]] that if the all-1/2 vector is in a matroid polyhedron, then the ground set of the matroid can be covered by 2 bases. This implies that the above conjecture is true if every vertex of ''P'' has only even coordinates. A possible strengthening is the following. '''Question.''' Is it true that if all vertices of an integer [[g-polymatroid]] ''Q'' are in <math>\{0,1,-1\}^n</math> and <math>0 \in Q</math>, then ''Q'' has a vertex ''v'' such that ''-v'' is in ''Q''?
==References==
