On unimodular tournaments
A tournament is unimodular if the determinant of its skew-adjacency matrix is \(1\). In this paper, we give some properties and constructions of unimodular tournaments. A unimodular tournament \(T\) with skew-adjacency matrix \(S\) is invertible if \(S^{-1}\) is the skew-adjacency matrix of a tourna...
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| Veröffentlicht in: | arXiv.org 2021-09 |
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| creator | Belkouche, Wiam Boussaïri, Abderrahim Chaïchaâ, Abdelhak Lakhlifi, Soufiane |
| description | A tournament is unimodular if the determinant of its skew-adjacency matrix is \(1\). In this paper, we give some properties and constructions of unimodular tournaments. A unimodular tournament \(T\) with skew-adjacency matrix \(S\) is invertible if \(S^{-1}\) is the skew-adjacency matrix of a tournament. A spectral characterization of invertible tournaments is given. Lastly, we show that every \(n\)-tournament can be embedded in a unimodular tournament by adding at most \(n - \lfloor\log_2(n)\rfloor\) vertices. |
| doi_str_mv | 10.48550/arxiv.2109.11809 |
| format | Article |
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| subjects | Apexes Graphs Mathematics - Combinatorics Tournaments & championships |
| title | On unimodular tournaments |
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