Abstract:The oriented Ramsey number r(H) for an acyclic digraph H is the minimum integer n such that any n-vertex tournament contains a copy of H as a subgraph. We prove that the 1-subdivision of the k-vertex transitive tournament H k satisfies r(H k ) ≤ O(k 2 log log k). This is tight up to multiplicative log log k-term.We also show that if T is an n-vertex tournament with ∆ + (T )arcs. This is also tight up to multiplicative constant.2 for an n-vertex graph G to contains H as a subgraph was determined by Erdős-Stone … Show more
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