On the number of maximal independent sets and maximal induced bipartite subgraphs in $K_4$-free graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914214353829888 |
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| author | Hartel, Thilo Picasarri-Arrieta, Lucas Rautenbach, Dieter |
| author_facet | Hartel, Thilo Picasarri-Arrieta, Lucas Rautenbach, Dieter |
| contents | Let $G$ be a $K_4$-free graph of order $n$ and let $k$ be an integer with $0\leq k\leq n$. We show the existence of positive constants $η$ and $ν$ such that $G$ has at most $(4-η)^{(5-η)k-n}(5-η)^{n-(4-η)k}$ maximal independent sets of order $k$ and at most $O\left((12-ν)^{\frac{n}{4}}\right)$ maximal induced bipartite subgraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19356 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the number of maximal independent sets and maximal induced bipartite subgraphs in $K_4$-free graphs Hartel, Thilo Picasarri-Arrieta, Lucas Rautenbach, Dieter Combinatorics Let $G$ be a $K_4$-free graph of order $n$ and let $k$ be an integer with $0\leq k\leq n$. We show the existence of positive constants $η$ and $ν$ such that $G$ has at most $(4-η)^{(5-η)k-n}(5-η)^{n-(4-η)k}$ maximal independent sets of order $k$ and at most $O\left((12-ν)^{\frac{n}{4}}\right)$ maximal induced bipartite subgraphs. |
| title | On the number of maximal independent sets and maximal induced bipartite subgraphs in $K_4$-free graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.19356 |