Ramsey Property And Algebraic Property Of Hypergraph

As a generalization of graph, Hypergraph, especially uniform hypergraph has a great application on describing problems from daily life. In this paper, we mainly discuss the Ramsey property and Algebraic property of uniform hypergraph. First, we obtain the lower bound of the independent number and asymptotic lower bound on symmetric and asymmetric form of Ramsey number by the probabilistic method and Lovasz Local Lemma, which were commonly used in the studying of Graph Theory. In addition, a result on multicolor Ramsey number of uniform hypergraph is presented. Second, we focus on the Algebraic property of uniform hypergraph. We discussed the spectral radius of hypergraphs through the row sum of the corresponding incidence matrix and the well-known Perron-Frobenius theorem. Another result on the lower bound of uniform hypergraph is obtained by introducing the similar matrix which has the same eigenvalues and eigenvectors with the original matrix.