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Showing 1 to 3 of 3 for “"Online Ramsey"”.
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Games on Graphs and Other Combinatorial Problems
… Chapter 5, we consider the so-called restricted online Ramsey numbers, which correspond to a certain colouring game in the Builder-Painter setup. We provide a tight lower bound for the restricted online Ramsey numbers of matchings as long as the number of the allowed colours is small, resolving …
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Extremal Problems for Cycles, Paths and Set-Systems
… main tool (the Key Lemma) for proving results on Ramsey-type problems about cycles in sparse random graphs. In Chapter 3 we count at least how many Hamilton cycles one can find in a hypergraph which is guaranteed to contain at least one. For $0\leq \ell <k$, a Hamilton $\ell$-cycle in a …
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Topics in Probabilistic Combinatorics
… in graphs. In Chapter 5, we investigate the online Ramsey number of paths, showing that for every $k\ge 10$, the online Ramsey number for paths $P_k$ and $P_n$ satisfies $\tilde{r}(P_k,P_n) \geq \frac{5}{3}n + \frac{k}{9} - 4$. This matches up to a linear term in $k$ the upper bound recently …