Abstract
For a family $\mathcal{H}$ of graphs, a graph $G$ is said to be $\mathcal{H}$-free if $G$ contains no member of $\mathcal{H}$ as an induced subgraph. Let $\mathcal{G}_2^{(3)}}(\mathcal{H})$ denote the family of $2$-connected $\mathcal{H}$-free graphs having minimum degree at least $3$. This paper is concerned with families $\mathcal{H}$ of connected graphs with $|\mathcal{H}| = 3$ such that $\mathcal{G}_2^{(3)}}(\mathcal{H})$ is a finite family. In particular, we show that for a connected graph $T$ of order at least $3$ that is not a star, $\mathcal{G}_2^{(3)}(\{K_4,K_{2,2},T\})$ is finite if and only if $T$ is a path of order at most $6$.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Kotani, Takafumi and Egawa, Yoshimi
(2025)
"Forbidden triples for $2$-connected graphs with minimum degree three which contain $K_4$ and $K_{2,2}$,"
Theory and Applications of Graphs: Vol. 12:
Iss.
2, Article 5.
DOI: 10.20429/tag.2025.120205
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol12/iss2/5
Supplemental Dois