2 problems

Let $J$ be an $m\times n$ pattern, and let ${\mathcal A}$ be a partial matrix over $J$. Associate to $J$ the bipartite graph $G_J$ with row vertices and column vertices, putting an…

Let ${\mathcal A}$ be a partial matrix over a field, and let its associated bipartite graph be the graph whose two vertex classes index the rows and columns of ${\mathcal A}$, with…