### Unavoidable Induced Subgraphs of 2-Connected Graphs

- Series
- Graph Theory Seminar
- Time
- Tuesday, April 11, 2023 - 15:45 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Sarah Allred – Vanderbilt University – sarah.e.allred@vanderbilt.edu

Ramsey proved that for every positive integer r, every sufficiently large graph contains as an induced subgraph either a complete graph on r vertices or an independent set with r vertices. It is well known that every sufficiently large, connected graph contains an induced subgraph isomorphic to one of a large complete graph, a large star, and a long path. We prove an analogous result for 2-connected graphs. Similarly, for infinite graphs, every infinite connected graph contains an induced subgraph isomorphic to one of the following: an infinite complete graph, an infinite star, and a ray. We also prove an analogous result for infinite 2-connected graphs.