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- Title
Bounds on Ramsey games via alterations.
- Authors
Guo, He; Warnke, Lutz
- Abstract
We present a refinement of the classical alteration method for constructing H $H$‐free graphs for suitable edge‐probabilities p $p$, we show that removing all edges in H $H$‐copies of the binomial random graph Gn,p ${G}_{n,p}$ does not significantly change the independence number. This differs from earlier alteration approaches of Erdős and Krivelevich, who obtained similar guarantees by removing one edge from each H $H$‐copy (instead of all of them). We demonstrate the usefulness of our refined alternation method via two applications to online graph Ramsey games, where it enables easier analysis.
- Subjects
RANDOM graphs; RAMSEY theory; GAMES; VIDEO games
- Publication
Journal of Graph Theory, 2023, Vol 104, Issue 3, p470
- ISSN
0364-9024
- Publication type
Article
- DOI
10.1002/jgt.22973