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Master's Dissertation
DOI
10.11606/D.45.2007.tde-11062007-012359
Document
Author
Full name
Fabricio Siqueira Benevides
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2007
Supervisor
Committee
Kohayakawa, Yoshiharu (President)
Feofiloff, Paulo
Moreira, Carlos Gustavo Tamm de Araujo
Title in Portuguese
Teoria de Ramsey para circuitos e caminhos
Keywords in Portuguese
caminhos
circuitos
Ramsey
regularidade
Abstract in Portuguese
Os principais objetos de estudo neste trabalho são os números de Ramsey para circuitos e o lema da regularidade de Szemerédi. Dados grafos $L_1, \ldots, L_k$, o número de Ramsey $R(L_1,\ldots,L_k)$ é o menor inteiro $N$ tal que, para qualquer coloração com $k$ cores das arestas do grafo completo com $N$ vértices, existe uma cor $i$ para a qual a classe de cor correspondente contém $L_i$ como um subgrafo. Estaremos especialmente interessados no caso em que os grafos $L_i$ são circuitos. Obtemos um resultado original solucionando o caso em que $k=3$ e $L_i$ são circuitos pares de mesmo tamanho.
Title in English
Ramsey theory for cycles and paths
Keywords in English
cycles
paths
Ramsey
regularity
Abstract in English
The main objects of interest in this work are the Ramsey numbers for cycles and the Szemerédi regularity lemma. For graphs $L_1, \ldots, L_k$, the Ramsey number $R(L_1, \ldots,L_k)$ is the minimum integer $N$ such that for any edge-coloring of the complete graph with~$N$ vertices by $k$ colors there exists a color $i$ for which the corresponding color class contains~$L_i$ as a subgraph. We are specially interested in the case where the graphs $L_i$ are cycles. We obtained an original result solving the case where $k=3$ and $L_i$ are even cycles of the same length.
 
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Dissertacao.pdf (613.68 Kbytes)
Publishing Date
2007-10-15
 
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