Bounds on Ramsey Games via Alterations

Abstract

We present a refinement of the classical alteration method for constructing $H$-free graphs: for suitable edge-probabilities $p$, we show that removing all edges in $H$-copies of the binomial random graph $G_{n,p}$ 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 $H$-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.

10 pages; minor edits; to appear in the Journal of Graph Theory

References in corpus (2)

• Upper tail bounds for Stars
• On the power of random greedy algorithms

Cited by in corpus (1)

• Note on down-set thresholds