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Ramsey Property and Algebraic Property of Hypergraph

Author: TangWenLiang
Tutor: LiYuSheng
School: Hohai University
Course: Applied Mathematics
Keywords: Uniform hypergraph Ramsey nature Algebraic properties Local lemma Spectral radius
CLC: O157.6
Type: Master's thesis
Year: 2006
Downloads: 84
Quote: 0
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Abstract


As a general diagram was to promote hypergraph especially uniform hypergraph able to better portray real life issues . This paper focuses on the the uniform hypergraph Ramsey nature algebraic properties . First using probabilistic methods commonly used in modern graph theory research and Lovász local lemma , we obtain a lower bound independent of the number of uniform hypergraph symmetric and asymmetric two-color Ramsey number of lower bound estimates , also Multicolor Ramsey Numbers the lower bound . The another main content of this article is consistent ultra Spectral Radius discussion . Perron-Frobenius theorem us through discussion agreed ultra Figure adjacency matrix of the line and to study diagram of the spectral radius , at the same time also the introduction of a hypergraph adjacency matrix similar to the matrix through research similar to the root of the matrix eigenvalue to analyze the original matrix of characteristic roots , also to get a better result .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > The application of graph theory
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