Relations Among The Parameters Of Hypergraphs And Colourings Of Hypergraphs

Hypergraphs are the generalization of graphs. In this thesis the relations among the parameters of hypergraphs and colourings of hypergraphs are discussed .This thesis consists of four chapters.In Chapter 1, the importance of studying the relations among the parameters of hypergraphs and colourings of hypergraphs are stated , also the main concepts notions of hypergraphs (for example (H) a(H), v(H), r(H), p(H), ar(H) Dr(H) Dv(H), De(H), x (H), (H), ([H]2) etc.) and some research results are shown.In Chapter 2, the relations between the independence numbers of// and H are studied, and some results are gotten, where 77 be a complementary hypergraph of an uniform hypergraph H.For every r- uniform hypergraph H, We have:In Chapter 3, the relations among the dominating numbers independence numbers and covering numbers of hypergraphs are studied, and some results are obtained.For every hypergraph H, We have :For every r- uniform hypergraph H, We have:In Chapter 4, the exact upper bound of the number of edges of linear intersecting hypergraphs is given: Let H be a linear intersecting hypergraph, thenmthenw which generalisesfamous theorems of de Bruijn, Erdos[3] and Fiiredi[14].