Think about it this way: a graph whose edges have been painted with red and blue and where the ONLY clique you find is in red cannot satisfy both R(3,4) and R(4,3), which we know it must.

## There is a subtle difference...

Think about it this way: a graph whose edges have been painted with red and blue and where the ONLY clique you find is in red cannot satisfy both R(3,4) and R(4,3), which we know it must.