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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.10996 |
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| _version_ | 1866914758117031936 |
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| author | Egawa, Yoshimi Furuya, Michitaka |
| author_facet | Egawa, Yoshimi Furuya, Michitaka |
| contents | For a family $\mathcal{H}$ of graphs, a graph $G$ is said to be {\it $\mathcal{H}$-free} if $G$ contains no member of $\mathcal{H}$ as an induced subgraph. We let $\tilde{\mathcal{G}}_{3}(\mathcal{H})$ denote the family of connected $\mathcal{H}$-free graphs having minimum degree at least $3$. In this paper, we characterize the non-caterpillar trees $T$ having diameter at least $7$ such that $\tilde{\mathcal{G}}_{3}(\{C_{3},C_{4},T\})$ is a finite family, where $C_{n}$ is a cycle of order $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Forbidden subgraphs generating a finite set of graphs with minimum degree three and large girth Egawa, Yoshimi Furuya, Michitaka Combinatorics For a family $\mathcal{H}$ of graphs, a graph $G$ is said to be {\it $\mathcal{H}$-free} if $G$ contains no member of $\mathcal{H}$ as an induced subgraph. We let $\tilde{\mathcal{G}}_{3}(\mathcal{H})$ denote the family of connected $\mathcal{H}$-free graphs having minimum degree at least $3$. In this paper, we characterize the non-caterpillar trees $T$ having diameter at least $7$ such that $\tilde{\mathcal{G}}_{3}(\{C_{3},C_{4},T\})$ is a finite family, where $C_{n}$ is a cycle of order $n$. |
| title | Forbidden subgraphs generating a finite set of graphs with minimum degree three and large girth |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.10996 |