Unavoidable Induced Subgraphs of Large 2Connected Graphs
Abstract
Ramsey proved that for every positive integer $n$, every sufficiently large graph contains an induced $K_n$ or $\overline{K}_n$. Among the many extensions of Ramsey's Theorem there is an analogue for connected graphs: for every positive integer $n$, every sufficiently large connected graph contains an induced $K_n$, $K_{1,n}$, or $P_n$. In this paper, we establish an analogue for 2connected graphs. In particular, we prove that for every integer exceeding two, every sufficiently large 2connected graph contains one of the following as an induced subgraph: $K_n$, a subdivision of $K_{2,n}$, a subdivision of $K_{2,n}$ with an edge between the two vertices of degree $n$, and a welldefined structure similar to a ladder.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 arXiv:
 arXiv:2009.12503
 Bibcode:
 2020arXiv200912503A
 Keywords:

 Mathematics  Combinatorics;
 05C75;
 05C55
 EPrint:
 15 pages