The maximal eigenvalue of 0-1 matrices with prescribed number of ones
The author determines the maximum spectral radius for a class of (0,1) matrices with a specified shape and specified number of ones, and for a class of symmetric (0,1) matrices with specified shape, zero diagonal, and a specified number of ones. The number of ones is restricted in certain ways, and a conjecture covering more configurations is stated. The paper is richly detailed with numerous (sometimes technical) ideas and other results. This problem was motivated by previous work of \textit{R. Brualdi} and \textit{A. Hoffman} [On the spectral radius of (0,1) matrices. (to appear)], and stems initially from ideas of \textit{B. Schwarz} [Duke Math. J. 31, 45-62 (1964; Zbl 0121.264)].
scientific article; zbMATH DE number 3925008