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Combinatorial ranks of matrices. (English) Zbl 0980.05025
Summary: In matrix form we provide graph theoretical results that are related to the ranks of matrices and to perfect graphs. The proofs are all based on basic and well-known linear algebraic facts. We give a new proof of the perfect graph theorem of Lovász.
MSC:
05C15 Coloring of graphs and hypergraphs
05C17 Perfect graphs
15A15 Determinants, permanents, traces, other special matrix functions
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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