• Title, Summary, Keyword: bipartite tournament matrices

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ON BIPARTITE TOURNAMENT MATRICES

  • Koh, Youngmee;Ree, Sangwook
    • Korean Journal of Mathematics
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    • v.7 no.1
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    • pp.53-60
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    • 1999
  • We find bounds of eigenvalues of bipartite tournament matrices. We see when bipartite matrices exist and how players and teams of the matrices are evenly ranked. Also, we show that a bipartite tournament matrix can be both regular and normal when and only when it has the same team size.

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SPECTRAL PROPERTIES OF BIPARTITE TOURNAMENT MATRICES

  • Koh, Young-Mee;Ree, Sang-Wook
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.183-190
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    • 2001
  • In this paper, we look at the spectral bounds of a bipartite tournament matrix M with arbitrary team size. Also we find the condition for the variance of the Perron vector of M to vanish.

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THE ORDER OF CYCLICITY OF BIPARTITE TOURNAMENTS AND (0, 1) MATRICES

  • Berman, Abraham;Kotzig, Anton
    • Kyungpook Mathematical Journal
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    • v.19 no.1
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    • pp.127-134
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    • 1979
  • A (0,1) matrix is acyclic if it does not have a permutation matrix of order 2 as a submatrix. A bipartite tournament is acyclic if and only if its adjacency matrix is acyclic. The concepts of (maximal) order of cyclicity of a matrix and a bipartite tournament are introduced and studied.

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