Bulletin of the
Korean Mathematical Society BKMS

For positive integral vectors $R=(r_1,\cdots,r_m)$ and $S=(s_1,\cdots,s_n)$, we consider the class ${\Cal U}(R,S)$ of all $m\times n$ matrices of 0's and 1's with row sum vector $R$ and column sum vector $S$. Let $\overline{{\Cal U}(R,S)}$ denote the convex hull of ${\Cal U}(R,S)$. A vector $E_m$ denote the $m$-tuple of 1's. Let $R=E_m$ and $S=(s_1,\cdots,s_n)$ with $s_1+\cdots+s_n=m$. In this paper, we consider a linear transformations that preserve the assignment on $\overline{{\Cal U}(R,S)}$.

Keywords: assignment function, linear preserver, bipartite graph

MSC numbers: 05C50, 15A04