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http://dx.doi.org/10.4134/JKMS.2005.42.4.871

ON KRAMER-MESNER MATRIX PARTITIONING CONJECTURE  

Rho, Yoo-Mi (Department of Mathematics Incheon University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.4, 2005 , pp. 871-881 More about this Journal
Abstract
In 1977, Ganter and Teirlinck proved that any $2t\;\times\;2t$ matrix with 2t nonzero elements can be partitioned into four sub-matrices of order t of which at most two contain nonzero elements. In 1978, Kramer and Mesner conjectured that any $mt{\times}nt$ matrix with kt nonzero elements can be partitioned into mn submatrices of order t of which at most k contain nonzero elements. In 1995, Brualdi et al. showed that this conjecture is true if $m = 2,\;k\;\leq\;3\;or\;k\geq\;mn-2$. They also found a counterexample of this conjecture when m = 4, n = 4, k = 6 and t = 2. When t = 2, we show that this conjecture is true if $k{\leq}5$.
Keywords
partition of matrices; bipartite graphs; adjacency matrices; matrix-crossings; P$^3$-claws; trees; unicyclic graphs;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
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