Some Topics On K-Perfect Hypergraphs

The motivations of this thesis are Lovasz'work and Berge's work on perfect graphs,which show the properties and concerned theorems of perfect graphs in detail. A graph G is perfect if G and each of its induced subgraphs have the property that the chromatic number Χ equals the size of a maximum clique ω. The idea of perfect graphs, due to C.Berge(1961),has been one of the most fruitful in graph theory, and during that period,there were two important conjectures,namely,the weak perfect graph and the strong perfect graph, which have been proved to be theorems now.As we all know that hypergraphs are more generalizable than graphs,the form of graphs is a special case of that of hypergraphs.Hence,according to the characteristics of the perfectness of graphs,I want to discuss the perfectness of hypergraphs.However,the perfectness of graphs can not be transformed to that of hypergraphs parallelly.Therefore,on one hand,we consider the perfectness of graphs as the basis of this paper.On the other hand.some new definitions about perfectness of hypergraphs are made.A hypergraph is defined to be a family of hyperedges which are sets of vertices of cardinality not necessarily 2(as for graphs). In this thesis,we consider only finite hypergraphs H = {E₁, E₂, ? ? ? , E_m} on X = {x₁, X₂, ? ? ?, x_n}o The following are my main results:...