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The maximum order of reduced square (0,1)-matrices with a given rank

Haemers,W.H.
; 
Peeters,M.J.P.
Abstract
The maximum order of a square (0, 1)-matrix A with a fixed rank r is considered, provided A has no repeated rows or columns. When A is the adjacency matrix of a graph, Kotlov and Lovász [A. Kotlov and L. Lovász. The rank and size of graphs. J. Graph Theory, 23:185–189, 1996.] proved that the maximum order equals Θ(2r/2). In this note, it is showed that this result remains correct if A is symmetric, but becomes false if symmetry is not required.
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Appeared earlier as CentER Discussion Paper 2011-113
Date
2012
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Tilburg University Research Output Collection
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Haemers, W H & Peeters, M J P 2012, 'The maximum order of reduced square (0,1)-matrices with a given rank', Electronic Journal of Linear Algebra, vol. 24, pp. 3-6.
URI
https://hdl.handle.net/20.500.14602/57336
License
info:eu-repo/semantics/restrictedAccess
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