edge [len=2,penwidth=1.5] node [label="",shape=point,width=.1,height=.1] 1--2 [color=red] 1--3 [color=red] 1--4 [color=blue] 1--5 [color=blue] 2--3 [color=blue]...
Diagram of a 2-coloured K_5 without a monochromatic K_3....
