% gr-Ramsey.tex -- R(3,3) = 6
% left : K5 coloured without monochromatic triangle
% right : in K6, every colouring has a monochromatic triangle
% Engine : pdfLaTeX or LuaLaTeX
\documentclass[border=3mm, convert=false]{standalone}
\usepackage{tkz-berge}
\begin{document}
\begin{tikzpicture}
  \GraphInit[vstyle=Art]
  \SetGraphUnit{2.2}
  \Vertices[rotation=90]{circle}{0,1,2,3,4}
  \Edges[local,color=red,lw=1.5pt](0,1,2,3,4,0)
  \Edges[local,color=blue,lw=1.5pt](0,2,4,1,3,0)
  \Vertices[rotation=90]{circle}{0,1,2,3,4}
  \node at (0,-3) {\(K_5\) : no monochromatic triangle};
  \begin{scope}[xshift=7cm]
    \Vertices[rotation=90]{circle}{a,b,c,d,e}
    \Vertex[x=0,y=0]{f}
    \Edges[local,color=red,lw=1.5pt](a,b,c,d,e,a)
    \Edges[local,color=blue,lw=1.5pt](a,c,e,b,d,a)
    \foreach \v in {a,b}{\Edge[local,color=red,lw=1.5pt](f)(\v)}
    \foreach \v in {c,d,e}{\Edge[local,color=blue,lw=1.5pt](f)(\v)}
    \fill[red,opacity=.25] (f.center) -- (a.center) -- (b.center) -- cycle;
    \Vertices[rotation=90]{circle}{a,b,c,d,e}
    \Vertex[x=0,y=0]{f}
    \node at (0,-3) {\(K_6\) : the triangle \(f a b\) is red};
  \end{scope}
\end{tikzpicture}
\end{document}