Looking for some hints on a homework problem. As far as I know, it's not from any textbook.
Color the vertices of $K_n$, the complete graph on $n$ vertices, red or blue. For how many $n$ will there be no monochromatic triangles (vertices all the same color). Note this question is not the one about coloring the edges.
My conjecture: for $n\ge 5$, there will always be a red or blue triangle.
I'm hoping the "pigeonhole principle" will apply somewhere. I don't think the instructor is asking us to delve into Ramsey theory.
Thanks in advance.