Induced Cycles of Many Lengths
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908818065063936 |
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| author | Chudnovsky, Maria Maier, Ilya |
| author_facet | Chudnovsky, Maria Maier, Ilya |
| contents | Let $G$ be a graph and let $\mathrm{cl}(G)$ be the number of distinct induced cycle lengths in $G$. We show that for $c,t\in \mathbb N$, every graph $G$ that does not contain an induced subgraph isomorphic to $K_{t+1}$ or $K_{t,t}$ and satisfies $\mathrm{cl}(G) \le c$ has bounded treewidth. As a consequence, we obtain a polynomial-time algorithm for deciding whether a graph $G$ contains induced cycles of at least three distinct lengths. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_06874 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Induced Cycles of Many Lengths Chudnovsky, Maria Maier, Ilya Combinatorics Discrete Mathematics Data Structures and Algorithms Let $G$ be a graph and let $\mathrm{cl}(G)$ be the number of distinct induced cycle lengths in $G$. We show that for $c,t\in \mathbb N$, every graph $G$ that does not contain an induced subgraph isomorphic to $K_{t+1}$ or $K_{t,t}$ and satisfies $\mathrm{cl}(G) \le c$ has bounded treewidth. As a consequence, we obtain a polynomial-time algorithm for deciding whether a graph $G$ contains induced cycles of at least three distinct lengths. |
| title | Induced Cycles of Many Lengths |
| topic | Combinatorics Discrete Mathematics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2602.06874 |