The real symmetric matrices with a given rank and a P-set with maximum size

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Zhibin Du, Carlos M. da Fonseca

Published: 01 Jan 2025, Last Modified: 06 Jun 2025Discret. Math. 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Given a real symmetric matrix A of rank r, the maximum size of a P-set of A does not exceed ⌊r/2⌋. In this work, we fully characterize the maximal graphs for which there is a real symmetric matrix attaining this bound.