The Maximum Order of Reduced Square(0, 1)-Matrices with a Given Rank
AbstractWe look for the maximum order of a square (0, 1)-matrix A with a fixed rank r, provided A has no repeated rows or columns. If A is the adjacency matrix of a graph, Kotlov and Lovász [J. Graph Theory 23, 1996] proved that the maximum order equals Θ(2r/2). In this note we show that this result remains correct if A is symmetric, but becomes false if symmetry is not required.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-113.
Date of creation: 2011
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(0; 1)-matrix; rank; graph;
Find related papers by JEL classification:
- C0 - Mathematical and Quantitative Methods - - General
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- NEP-ALL-2011-11-07 (All new papers)
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