The evolution of unavoidable bi-chromatic patterns and extremal cases of balanceability

Yair Caro, Adriana Hansberg, Amanda Montejano

We study the color patterns that, for $n$ sufficiently large, are unavoidable in $2$-colorings of the edges of a complete graph $K_n$ with respect to $\min \{e(R),e(B)\}$, where $…