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Currently displaying 1 – 2 of 2

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Landau's and Rado's theorems and partial tournaments.

Brualdi, Richard A.; Kiernan, Kathleen — 2009

The Electronic Journal of Combinatorics [electronic only]

Hall exponents of matrices, tournaments and their line digraphs

Richard A. Brualdi; Kathleen P. Kiernan — 2011

Czechoslovak Mathematical Journal

Let $A$ be a square $(0, 1)$ -matrix. Then $A$ is a Hall matrix provided it has a nonzero permanent. The Hall exponent of $A$ is the smallest positive integer $k$ , if such exists, such that $A^{k}$ is a Hall matrix. The Hall exponent has received considerable attention, and we both review and expand on some of its properties. Viewing $A$ as the adjacency matrix of a digraph, we prove several properties of the Hall exponents of line digraphs with some emphasis on line digraphs of tournament (matrices).

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