Tree in forbidden triples generating a finite set of graphs with high connectivity

Abstract

For a graph and a set of connected graphs, is said be -free if does not contain any member of as an induced subgraph. For , we let denote the set of all -connected -free graphs. This paper is concerned with integers , and and a tree such that is finite. Among other results, we show that for integers , , and with , and , the diameter of a tree such that is finite is bounded above by a constant which depends only on but not on , or .

Keywords

• forbidden subgraph
• forbidden triple
• -connected graph