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- W2919235254 abstract "Given an acyclic oriented graph $vec{H}$ and a graph $G$, we write $G to vec{H}$ if every orientation of $G$ has an oriented copy of $vec{H}$. We define $vec{R}(vec{H})$ as the smallest number $n$ such that there exists a graph $G$ satisfying $G to vec{H}$. Denoting by $R(H)$ the classical Ramsey number of a graph $H$, we show that $vec{R}(vec{H}) leq 2R(H)^{c log^2 h}$ for every acyclic oriented graph $vec{H}$ with $h$ vertices, where $H$ is its underlying undirected graph. We also study the threshold function for the event ${G(n,p) to vec{H}}$ in the binomial random graph $G(n,p)$. Finally, we consider the isometric case, in which we require that, for every two vertices $x, y in V(vec{H})$ and their respective copies $x', y'$ in $vec{G}$, the distance between $x$ and $y$ is equal to the distance between $x'$ and $y'$. We prove an upper bound for the isometric Ramsey number of an acyclic orientation of the cycle, applying the hypergraph container lemma in random graphs." @default.
- W2919235254 created "2019-03-11" @default.
- W2919235254 creator A5009822741 @default.
- W2919235254 date "2019-03-05" @default.
- W2919235254 modified "2023-09-27" @default.
- W2919235254 title "Ramsey-type problems in orientations of graphs" @default.
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