Triangle-free graphs and completely positive matrices

Central European Journal of Operations Research（2021）

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Abstract

Completely positive matrices are matrices that can be decomposed as BB^T , where B is an entrywise nonnegative matrix. These matrices have many applications, including applications to optimization. This article is a survey of some results in the theory of completely positive matrices that involve matrices whose graph contains no triangles.

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Key words

Triangle-free graph, Completely positive matrix, Cp-rank, Cp factorization, Minimal cp factorization, 15A23, 15B48

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