The Application Of The Probabilistic Methods In Hypergraph Two-Coloring

The Probabilistic Methods works as follows: Trying to prove that a structure with certain desired properties, one defines an appropriate probability space of structures and then shows that the desired properties hold in this space with positive probability. Hence, some good structures exist. Paul Erd?s earlier used the Methods in hypergraph two-coloring. An n-uniform hypergraphH has PropertyB if given any two-coloring of the underlying points some edges are monochromatic. Erd?s defined the function m ( n )as the minimal size of an n-uniform hypergraph which has PropertyB . Then gived the upper and lower bounds of m ( n ). On this basis, We further discuss the problem of hypergraph balanced coloring. An n-uniform hypergraphH has Property Bb if given any two-coloring of the underlying points some edges are unbalanced. We defined the function mb ( n )as the minimal size of an n-uniform hypergraph which has Property Bb . At last give the upper and lower bounds of mb ( n ).