| Autor: |
François Pitois, Mohammed Haddad, Hamida Seba, Olivier Togni |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
Discrete Mathematics & Theoretical Computer Science, Vol vol. 25:3 special issue..., Iss Special issues (2024) |
| Druh dokumentu: |
article |
| ISSN: |
1365-8050 |
| DOI: |
10.46298/dmtcs.10751 |
| Popis: |
Inspired by the split decomposition of graphs and rank-width, we introduce the notion of $r$-splits. We focus on the family of $r$-splits of a graph of order $n$, and we prove that it forms a hypergraph with several properties. We prove that such hypergraphs can be represented using only $\mathcal O(n^{r+1})$ of its hyperedges, despite its potentially exponential number of hyperedges. We also prove that there exist hypergraphs that need at least $\Omega(n^r)$ hyperedges to be represented, using a generalization of set orthogonality. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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