2019
DOI: 10.1002/jgt.22445
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Online Ramsey theory for a triangle on ‐free graphs

Abstract: Given a class scriptC of graphs and a fixed graph H, the online Ramsey game for H on scriptC is a game between two players Builder and Painter as follows: an unbounded set of vertices is given as an initial state, and on each turn Builder introduces a new edge with the constraint that the resulting graph must be in scriptC, and Painter colors the new edge either red or blue. Builder wins the game if Painter is forced to make a monochromatic copy of H at some point in the game. Otherwise, Painter can avoid crea… Show more

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