Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  728.05059
Autor:  Erdös, Paul; Hajnal, András; Tuza, Zsolt
Title:  Local constraints ensuring small representing sets. (In English)
Source:  J. Comb. Theory, Ser. A 58, No.1, 78-84 (1991).
Review:  A set T is said to cover a set system F if T meets all members of F. We raise the following general problem. Find relations among the natural numbers p,r,s,t, that imply the truth of the following statement: If F is an r-uniform set system such that each of its subsystems on at most p elements can be covered with an s-element set, then F can be covered with a t-element set. Here we investigate the case s = 1.
Classif.:  * 05D15 Transversal (matching) theory
                   05A05 Combinatorial choice problems
                   05B40 Packing and covering (combinatorics)

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