For a graph Gand a set of connected graphs, G is said be -free if Gdoes not contain any member of as an induced subgraph. For we let denote the set of all k-connected -free graphs. This paper is concerned with integers and and a tree T such that is finite. Among other results, we show that is finite for every and every
-free if Gdoes not contain any member of 
we let 
denote the set of all k-connected 
-free graphs. This paper is concerned with integers 
and 
and a tree T such that 
is finite. Among other results, we show that 
is finite for every 
and every 
