Forbidden subgraphs generating a finite set of graphs with minimum degree three and large girth
| Autor: | Egawa, Yoshimi, Furuya, Michitaka |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $n$. Comment: 31 pages, 19 figures |
| Databáze: | arXiv |
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