A construction of Steiner Triple Systems of type $v\longrightarrow 2v+7$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912692886831104 |
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| author | Bonacini, Paola Gionfriddo, Mario Marino, Lucia |
| author_facet | Bonacini, Paola Gionfriddo, Mario Marino, Lucia |
| contents | A Steiner Triple System ($STS$) of order $v$ is a hypergraph uniform of rank 3, with $v$ vertices and such that every 2-subset of vertices has degree 1. In this paper we give a construction, by difference method, of type $v\longrightarrow 2v+7$ with $v=2^n-7$, which means that, given an $STS$ of order $v=2^n -7$, it is always possible to construct an $STS$ of order $2^{n+1}-7$. Through this construction it is possible to get for any $n\ge 5$ an $STS(2^n-7)$ with a maximal independent set of maximal cardinality and which is $(n-1)$-bicolorable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04823 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A construction of Steiner Triple Systems of type $v\longrightarrow 2v+7$ Bonacini, Paola Gionfriddo, Mario Marino, Lucia Combinatorics 05B07, 05B05, 05C15 A Steiner Triple System ($STS$) of order $v$ is a hypergraph uniform of rank 3, with $v$ vertices and such that every 2-subset of vertices has degree 1. In this paper we give a construction, by difference method, of type $v\longrightarrow 2v+7$ with $v=2^n-7$, which means that, given an $STS$ of order $v=2^n -7$, it is always possible to construct an $STS$ of order $2^{n+1}-7$. Through this construction it is possible to get for any $n\ge 5$ an $STS(2^n-7)$ with a maximal independent set of maximal cardinality and which is $(n-1)$-bicolorable. |
| title | A construction of Steiner Triple Systems of type $v\longrightarrow 2v+7$ |
| topic | Combinatorics 05B07, 05B05, 05C15 |
| url | https://arxiv.org/abs/2511.04823 |