On the Ramsey Property of Families of Graphs
On the Ramsey Property of Families of Graphs
For graphs $A$ and $B$ the relation $A \to (B)_r^1$ means that for every $r$-coloring of the vertices of $A$ there is a monochromatic copy of $B$ in $A$. $\operatorname {Forb} ({G_1},{G_2}, \ldots ,{G_n})$ is the family of graphs which do not embed any one of the graphs ${G_1},{G_2}, \ldots …