Abstract
A (0, 1) matrix is linear if it does not contain a 2 × 2 submatrix of all ones. In these two papers we deal with perfect graphs whose clique-node incidence matrix is linear. We first study properties of some subgraphs that contain odd holes. We then prove that a graph whose clique-node incidence matrix is linear but not totally unimodular contains a node v such that the removal of v and all its neighbors disconnects the graph. These results yield a proof of the strong perfect graph conjecture for this class of graphs.
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