Factorizing the Complete Graph into Factors with Large Star Number PAUL ERDŐS , NORBERT SAUER , AND JONATHAN SCHAER

If G is a graph such that for any set S of n vertices of G there exists a subgraph H of G which is a star and S C V(H) then G has star number (st .) n . The set of graphs {F1 , F2 , . . ., FL } is a decomposition of G into the factors F7 , 1 2 , . . ., Fl, if V(Fj) = V(G) (1 < i < k), E(Fj) n E(F,) _ 0 for all i 71-j, and Uk1 E(Fj) = E(G) . Letf (n, k) be the smallest number m such that the complete graph on m vertices can be decomposed into k factors of st . n . This problem or various specializations of it have so far been investigated in [1-6] . The best results are