
\documentclass[beamer]{standalone}
\usepackage{tikz}

\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{external}
\tikzexternalize % activate! 
\begin{document}
\begin{standaloneframe}

% If overlays do not work, use \only<1-n>{...} where n is the max overlay
 \only<1-4>{
  \begin{tikzpicture}[]
    \draw[color=white] (0, 4) -- (11,-4);
    % ...
    \coordinate (c) at (0,0);
    \coordinate (fb) at (10,-3);
    \coordinate (fh) at (10,3);

    \coordinate<2-> (p1) at (2,0);
    \coordinate<2-> (p2) at (4,-1);
    \coordinate<2-> (p3) at (4,1);

    \coordinate (r1) at (9,-2);
    \coordinate (r2) at (9,-1);
    \coordinate (r3) at (9,0);
    \coordinate (r4) at (9,2);

    \coordinate (p2r1) at (5,-1.5);
    \coordinate (p2r2) at (5,-0.5);
    \coordinate (p3r3) at (5,0.5);
    \coordinate (p3r4) at (5,1.5);
    
    \draw (fb) to[in=330, out=180] (c) to[out=30, in=180] (fh);

    \draw<2->[fill=black] (p1) circle (0.15);
    \draw<2->[fill=black] (p2) circle (0.15);
    \draw<2->[fill=black] (p3) circle (0.15);

    \draw<4->[color=red,fill=red] (r1) circle (0.15);
    \draw<4->[color=red,fill=red] (r2) circle (0.15);
    \draw<4->[color=red,fill=red] (r3) circle (0.15);
    \draw<4->[color=red,fill=red] (r4) circle (0.15);

    \draw<2-> (c) -- (p1);
    \draw<2-> (p2) -- (p1) -- (p3);

    \draw<4->[color=red] (p2) -- (p2r1);
    \draw<4->[color=red] (p2) -- (p2r2);
    \draw<4->[color=red] (p3) -- (p3r3);
    \draw<4->[color=red] (p3) -- (p3r4);
    
    \draw<4->[color=red,decorate, decoration=snake] (p2r1) to (r1);
    \draw<4->[color=red,decorate, decoration=snake] (p2r2) to (r2);
    \draw<4->[color=red,decorate, decoration=snake] (p3r3) to (r3);
    \draw<4->[color=red,decorate, decoration=snake] (p3r4) to (r4);

    \draw<3->[color=blue,dashed] (8,-3.1) -- (8, 3.1);
    \draw<3->[color=blue]  (8, 3.5) node {\Large$\ell$};
    \draw<4->[color=brown, dashed] (9,-3.1) -- (9, 3.1);
    \draw<4->[color=brown]  (9, 3.5) node {\Large$h$};


    \draw<2->[color=black]  (3.5, 0) node {\LARGE$F$};
    \draw<4->[color=red]  (10, 0) node {\LARGE$H$};

    % forall F exists c<k,\ell forall h>ell, \forall H\subseteq T(h), E\cup h\in S => f(E\cup H)=c
  \end{tikzpicture}
 }
\end{standaloneframe}
\end{document}
