Bounds on Ramsey Games via Alterations
He Guo, Lutz Warnke

TL;DR
This paper refines the alteration method for constructing $H$-free graphs in random graphs, showing that removing all edges in $H$-copies at suitable probabilities preserves independence number, and applies this to analyze online graph Ramsey games.
Contribution
It introduces a refined alteration technique that removes all edges in $H$-copies, improving analysis of $H$-free graphs and online Ramsey games.
Findings
Removing all edges in $H$-copies preserves independence number at certain probabilities.
The refined method simplifies analysis of online graph Ramsey games.
Demonstrates improved bounds and techniques for $H$-free graph construction.
Abstract
We present a refinement of the classical alteration method for constructing -free graphs: for suitable edge-probabilities , we show that removing all edges in -copies of the binomial random graph does not significantly change the independence number. This differs from earlier alteration approaches of Erd\H{o}s and Krivelevich, who obtained similar guarantees by removing one edge from each -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.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Computability, Logic, AI Algorithms
