Elsevier

Discrete Mathematics

Volume 104, Issue 1, 1 June 1992, Pages 23-47
Discrete Mathematics

Articulation sets in linear perfect matrices I: forbidden configurations and star cutsets☆

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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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☆

Partial support under NSF grants DMS 8606188 and ECS 8800281. This work was partly done while the authors were visiting IASI, Rome, in June 1986.

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