Extremal Problems and Random Processes on Graphs

Extremal Problems and Random Processes on Graphs

91 pages· 2008· ISBN 9780549957690
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This thesis is presented in three parts. In the first part, we analyze the following problem: let H be a finite tree. We consider trees T such that if the edges of T are colored so that no color occurs more than b times, then T has a subgraph isomorphic to H in which no color is repeated. We show that if H falls into a few classes of trees, including those of diameter at most 4, then the minimum value of e(T) is provided by a known construction, supporting a conjecture of Bohman, Frieze, Pikhurko and Smyth.

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