COVERING A GRAPH BY TOPOLOGICAL COMPLETE SUBGRAPHS

Every graph on n vertices can be covered by ex(n, TK4) =2n - 3 TK4-subgraphs and edges. A similar result might hold for arbitrary topological (complete) subgraphs as indicated by the following result: Every graph on n vertices can be covered by 65 ex(n, TKp)TKp-subgraphs and edges. If H is a connected graph (|H| ≥ 3) then every graph on n vertices can be covered by 400 ex(n, TH) TH-subgraphs and edges. Similar questions for coverings by odd and even cycles are also considered. © 1990 Springer-Verlag.