### Abstract

For a graph G and a set F of connected graphs, G is said be F-free if G does not contain any member of F as an induced subgraph. We let G_{3} (F) denote the set of all 3-connected F-free graphs. This paper is concerned with sets F of connected graphs such that |F| = 3 and G_{3}(F) is finite. Among other results, we show that for an integer m ≥ 3 and a connected graph T of order greater than or equal to 4, G_{3}({K_{4},K_{2,m}, T}) is finite if and only if T is a path of order 4 or 5.

Original language | English |
---|---|

Article number | 013 |

Journal | Electronic Journal of Combinatorics |

Volume | 22 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 Jul 17 |

### Keywords

- 3-connected graph
- Forbidden subgraph
- Forbidden triple

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Forbidden triples generating a finite set of 3-connected graphs'. Together they form a unique fingerprint.

## Cite this

Egawa, Y., Furuya, M., Fujisawa, J., Plummer, M. D., & Saito, A. (2015). Forbidden triples generating a finite set of 3-connected graphs.

*Electronic Journal of Combinatorics*,*22*(3), [013]. https://doi.org/10.37236/3255