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On-line Ramsey Theory for Bounded Degree Graphs
2011
Electronic Journal of Combinatorics
When graph Ramsey theory is viewed as a game, "Painter" 2-colors the edges of a graph presented by "Builder". Builder wins if every coloring has a monochromatic copy of a fixed graph $G$. In the on-line version, iteratively, Builder presents one edge and Painter must color it. Builder must keep the presented graph in a class ${\cal H}$. Builder wins the game $(G,{\cal H})$ if a monochromatic copy of $G$ can be forced. The on-line degree Ramsey number $\mathring {R}_\Delta(G)$ is the least $k$
doi:10.37236/623
fatcat:rx6c6374j5h4rgwhtnaqy6pa6m