Péter Ligeti

Erdős---Pyber Theorem for Hypergraphs and Secret Sharing

A new, constructive proof with a small explicit constant is given to the Erdős–Pyber theorem which says that the edges of a graph on

ANOTHER TWIST IN THE DINING CRYPTOGRAPHERS’ PROTOCOL

n

On an infinite family of graphs with information ratio 2 − 1/ k

n vertices can be partitioned into complete bipartite subgraphs so that every vertex is covered at most

Subwords in reverse-complement order

O(n/\log n)

On secret sharing and 3-uniform hypergraphs

O(n/logn) times. The theorem is generalized to uniform hypergraphs. Similar bounds with smaller constant value is provided for fractional partitioning both for graphs and for uniform hypergraphs. We show that these latter constants cannot be improved by more than a factor of 1.89 even for fractional covering by arbitrary complete multipartite subgraphs or subhypergraphs. In the case every vertex of the graph is connected to at least