[Tex/LaTex] Representing Hasse diagram of the Green order

Question

I need to represent graphs like the one below using xypics. They arise as the Hasse diagram of the Green order of finite semigroups (specifically finite Left Regular Bands) with the homomorphism to its support lattice. I know the very basics on how to draw lines and place points, but I don't know how one would draw ovaloids around a mass of points like in the image below. Also, I'd rather them not being ellipses.

Thank you for your time!

Answer 1

It's possible to use ellipse but it's better to use a rectangle with rounded corners and fit.

 \documentclass[11pt]{scrartcl}
 \usepackage{tikz}
 \usetikzlibrary{fit}

 \begin{document}
 \begin{tikzpicture}[y=1.5cm,
       every fit/.style={inner sep=4mm,orange,dashed,rounded corners=4mm,draw,line width=0.6mm}]

 \path (3,8)   coordinate  (s0)
       (1,6)   coordinate  (s1)  (5,6) coordinate (s2)
       (1,4)   coordinate  (s3)  (3,4) coordinate (s4)   (5,4) coordinate (s5)
       (0,2)   coordinate  (s6)  (1,2) coordinate (s7)   (2,2) coordinate (s8) (3,1.5) coordinate (s9) 
       (4,2.5) coordinate (s10)  (6,2) coordinate (s11);

  \node[fit=(s0)] (f1){}; \node[fit=(s1)(s2)](f2){}; \node[fit=(s3)(s5)](f3){};     
  \node[fit=(s6)(s9)(s10)(s11)](f4){};
  \node[right] at (f1.east) {$A$};   \node[right] at (f2.east) {$B$}; \node[right] at (f3.east) {$C$};
  \node[right] at (f4.east) {$D$};
  \draw[thick] (s0) -- (s1) -- (s3) -- (s6)
               (s1) -- (s4) -- (s7) (s4) -- (s8) (s4) -- (s9)
               (s0) -- (s2) -- (s5) -- (s11)  
               (s5) -- (s10);
  \draw[thick,double=black,draw=white]  (s2) -- (s3) (s2) to[out=-100 ,in=10] (s6);
  \foreach \i in {0,...,11} \draw[fill=blue!40]  (s\i) circle (2pt);
  \draw[->] (6,5) -- node [above]{$\theta$} (8,5);
  \path (9,8) coordinate   (t0)
        (9,6) coordinate   (t1)  
        (9,4) coordinate   (t2) 
        (9,2) coordinate   (t3) ;
   \draw[thick] (t0) -- (t1) -- (t2) -- (t3);
   \foreach \i in {0,...,3} \draw[fill=red!40]  (t\i) circle (2pt);
 \end{tikzpicture}
 \end{document}