Polymatroidal ideals and linear resolution

Let $S=K[x_1,ldots,x_n]$ be a polynomial ring over a field $K$ and $frak{m}=(x_1,ldots,x_n)$ be the unique homogeneous maximal ideal. ##Let $Isubset S$ be a monomial ideal with a linear resolution and $Ifrak{m}$ be a polymatroidal ideal. ##We prove that if either $Ifrak{m}$ is polymatroidal with strong exchange property, or $I$ is a monomial ideal in at most 4 variables, then $I$ is polymatroidal