论文标题
不可避免的大型2相互连接图的亚图
Unavoidable Induced Subgraphs of Large 2-Connected Graphs
论文作者
论文摘要
拉姆西证明，对于每个正整数$ n $，每个足够大的图都包含一个诱导的$ k_n $或$ \ overline {k} _n $。在Ramsey定理的许多扩展中，有一个用于连接的图形的类似物：对于每个正整数$ n $，每个足够大的连接图都包含诱导的$ k_n $，$ k_ {1，n} $或$ p_n $。在本文中，我们为2个连接图建立了一个类似物。特别是，我们证明，对于每个超过两个的整数，每个足够大的2个连接图都包含以下一个诱导子图：$ k_n $，一个$ k_ {2，n} $的细分，一个$ k_ {2，n} $的细分，具有两个vertices $ n $ $ n $ $ n $ ncord的effer and praind prainder and prainder and praind praind praind and praind pradection and praind prad and。
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 2-connected graphs. In particular, we prove that for every integer exceeding two, every sufficiently large 2-connected 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 well-defined structure similar to a ladder.
