 
Summary: Extremal Problems
Concerning
Transformations of
the Edges of the
Complete Hypergraphs
Yair Car0
SCHOOL OF MATHMAT/CS
UNlVERSITY OF T fLAVIV
RAM ATAV/V; TELAVIV, ISRAEL
ABSTRACT
We consider extremal problems concerning transformations of the
edges of complete hypergraphs. We estimate the order of the largest
subhypergraph K such that for every edge e E (K),f(e)e f ( K ) ,assum
ing f(e)# e. Several extensions and variations of this problem are also
discussed here.
INTRODUCTION
In this paper we investigate some extremal problems concerning transforma
tions of the nsubsets of a set.' We begin with some technical definitions.
For a set S, let IS1 denote its cardinality. For a graph G, let V(G)[respec
tively, E(G)]denote the vertex set (respectively, edge set) of G, and let e(G) =
