Example: LR constraints - Drawing and filling with arcs and Bezier curves

% LR constraints - Drawing and filling with arcs and Bezier curves
% Author: Henri Menke
\documentclass[tikz, border=10pt]{standalone}
\usetikzlibrary{calc}
\tikzset{
    vertex/.style = {
        circle,
        fill      = black,
        outer sep = 2pt,
        inner sep = 1pt,
    }
}
\begin{document}
\begin{tikzpicture}[>=stealth]
  % We need to adjust the bounding box manually
  % as the control points enlarge it.
  \path[use as bounding box] (-1,-0.5) rectangle (1.5,5.5);

  \coordinate (o) at (0,0);
  \node[below] at (o) {root};
  \draw node[vertex] (a) at (0,1) {};
  \draw node[vertex] (b) at (0,2) {};
  \draw node[vertex] (c) at (0,3) {};
  \draw node[vertex] (d) at (0,4) {};
  \node[above] at (d) {$v$};

  \draw (d) node[left] {$e_1$} -- (-0.5,4.5);
  \filldraw[draw=blue, fill=blue!50]
    (-0.5,4.5) .. controls (-1,5) and (-0.75,4.5) .. ($(c)+(180:4pt)$)
    arc[start angle=180, end angle=270, radius=4pt]
    -- ($(b)+(90:4pt)$) .. controls (-1,5) .. (-0.5,4.5);
  \draw (d) node[right] {$e_2$} -- (0.5,4.5);
  \filldraw[draw=red, fill=red!50]
    (0.5,4.5) .. controls (1,5) and (0.75,4.5) .. ($(c)+(0:4pt)$)
    arc[start angle=0, end angle=-90, radius=4pt]
    -- ($(b)+(90:4pt)$) arc[start angle=90, end angle=0, radius=4pt]
    ($(b)+(0:4pt)$) .. controls (1,5) .. (0.5,4.5);
  \draw[red, thick, ->] (0.5,4.5) .. controls (1,5) .. ($(b)+(0:4pt)$);
  \draw[->] (-0.5,4.5) .. controls (-1,5) and (3,7) .. (a);

  \draw[->] (o) -- (a) (a) -- (b) (b) -- (c) (c) -- node[left] {$e$} (d);
\end{tikzpicture}
\end{document}