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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2019
- DOI:
- 10.48550/arXiv.1909.02691
- arXiv:
- arXiv:1909.02691
- Bibcode:
- 2019arXiv190902691G
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics;
- 05C55;
- 05C80;
- 05D10;
- 05D40
- E-Print:
- 10 pages