Stability theorems for cancellative hypergraphs
A cancellative hypergraph has no three edges \(A,B,C\) with \(A\bigtriangleup B \subset C.\) The paper gives a short proof for Bollobás's result: the maximum size of a cancellative triple system is achieved by the balanced complete tripartite 3-graph. It also shows that the system \(F_5=\{abc,abd,cde\}\) (one of the two forbidden configurations in a cancellative hypergraph) itself enforces that maximum cardinality of a triple system, not containing a copy of \(F_5\), also achieved by the same extremal triple system (in case of \(n>32\), highly strengthening an earlier result of Frankl and Füredi). Finally it also proves stability results for both problems.
scientific article; zbMATH DE number 2104555
scientific article