Envy-free cake divisions cannot be found by finite protocols.
Equivalence of a Number-Theoretical Problem with a Problem from the Graph Theory
Erdös-Ko-Rado from intersecting shadows
A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős-Ko-Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corresponding results.
Erdős-Ko-Rado theorems for uniform set-partition systems.
Erdős-Ko-Rado-type theorems for colored sets.
Evolutionary families of sets.
Extremal problems for -partite and -colorable hypergraphs.
Extremal subsets of avoiding solutions to linear equations in three variables.