On 1-subdivisions of transitive tournaments

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The oriented Ramsey number (r) over right arrow (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 Hk satisfies (r) over right arrow (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 Delta+(T) - delta(+)(T) = O(n/k) - k(2), then T contains a 1-subdivision of (K) over right arrow (k), a complete k-vertex digraph with all possible k(k - 1) arcs. This is tight up to multiplicative constant.
Publisher
ELECTRONIC JOURNAL OF COMBINATORICS
Issue Date
2022-03
Language
English
Article Type
Article
Citation

ELECTRONIC JOURNAL OF COMBINATORICS, v.29, no.1

ISSN
1077-8926
DOI
10.37236/10788
URI
http://hdl.handle.net/10203/295870
Appears in Collection
MA-Journal Papers(저널논문)
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