There is another interesting way we might consider coloring edges, quite different from what we have discussed so far. What if we colored every edge of a graph either red or blue. Can we do so without, say, creating a monochromatic triangle (i.e., an all red or all blue triangle)? Certainly for some graphs the answer is yes. Try doing so for \(K_4\text{.}\) What about \(K_5\text{?}\) \(K_6\text{?}\) How far can we go?
in-context