Teoria de Ramsey para circuitos e caminhos / Ramsey theory for cycles and paths

AUTOR(ES)

Fabricio Siqueira Benevides

DATA DE PUBLICAÇÃO

2007

RESUMO

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.

ASSUNTO(S)

caminhos paths cycles regularity circuitos regularidade ramsey ramsey

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