On A Combinatorial Problem III

Abstract

A family of sets {Aα} is said by Miller [3] to have property B if there exists a set S which meets all the sets Aα and contains none of them. Property B has been extensively studied in several recent papers (see the references in [2] and the last chapter of P. Erdös and A. Hajnal, On chromatic number of graphs and set systems, Acta. Math. Acad. Sci. Hung. 17 (1966) 61–99).