Circling a collection of objects in a tree using xymatrix

Question

This code

\documentclass{amsart}
\usepackage[all]{xy}

\begin{document}

\[ 
\xymatrix@-0.75pc{
\overset{1}{\bullet}& & \overset{2}{\bullet}& & \overset{3}{\bullet}& &\overset{4}{\bullet} & &
\overset{5}{\bullet} & &\overset{6}{\bullet} & &\overset{7}{\bullet} & &\overset{8}{\bullet}  \\
&   \ar@{-}[ul] \overset{}{\bullet} \ar@{-}[ur]
& & & & \ar@{-}[ul] \overset{}{\bullet} \ar@{-}[ur]  & & & & \ar@{-}[ul] \overset{}{\bullet} 
\ar@{<..>}@/^1pc/[rrrr] \ar@{-}[ur] & & & & \ar@{-}[ul] \overset{}{\bullet} \ar@{-}[ur] &  \\
& & & \ar@{-}[ull] \overset{}{\bullet} \ar@{-}[urr]
& & & & & & & & 
\ar@{-}[ull]\overset{}{\bullet}\ar@{-}[urr] & & &  \\
& & & & & & & \ar@{-}[ullll] \overset{}{\bullet} 
\ar@{-}[urrrr]& & & & & & &  \\ 
}
\] 

\end{document}

is for the tree

but what I would like to add to the diagram are the circles as seen below:

which encapsulate the top two adjacent vertices, the two edges "connected" to them, and the vertex in the layer below, "connecting" the two edges. The circles can be decorated in any way, e.g., dotted or dashed, in any thickness and color, but is it possible to do this using xymatrix?

I suggest you to try to move to tikz instead of xy. It is much more powerful and intuitive. — Sigur, Feb 22 '19 at 15:53
@Sigur I tried tikz in the last few weeks but I'll try it again this weekend. Thanks! — Mee Seong Im, Feb 22 '19 at 16:45

score 4 · Accepted Answer · 2019-02-22T18:02:34.790

I'd use forest for that. (EDIT: made the dashed arrow more symmetric, thanks to @Sigur for pingng me!)

\documentclass{article}
\usepackage{forest}
\usetikzlibrary{fit}
\begin{document}
\begin{forest}
for tree={circle,fill,inner sep=2pt,outer sep=2pt,grow'=north,s sep=1cm
}
[
 [
  [,alias=A
   [,label=above:1,alias=1]
   [,label=above:2,alias=2]
  ]
  [,alias=B
   [,label=above:3,alias=3]
   [,label=above:4,alias=4]
  ]
 ]
 [
  [,alias=C
   [,label=above:5,alias=5]
   [,label=above:6,alias=6]
  ]
  [,alias=D
   [,label=above:7,alias=7]
   [,label=above:8,alias=8]
  ]
 ]
]
\node[circle,draw=cyan,inner sep=1pt,yshift=10pt,fit=(A) (1) (2)] (F1){};
\node[circle,draw=cyan,inner sep=1pt,yshift=10pt,fit=(B) (3) (4)] (F2) {};
\node[circle,draw=cyan,inner sep=1pt,yshift=10pt,fit=(C) (5) (6)] (F3) {};
\node[circle,draw=cyan,inner sep=1pt,yshift=10pt,fit=(D) (7) (8)] (F4) {};
\draw[dashed,latex-latex] (C.30) to[bend left] (D.150);
\end{forest}
\end{document}

NOTE: You could draw the full thing programmatically, meaning you do not have to punch in the numbers 1 to 8 and so on. But given that here this is not much effort, I leave it as is.

@Sigur Thanks! if I would change it, then to \draw[dashed,latex-latex] (C.30) to[bend left] (D.150);. — , Feb 22 '19 at 18:00

Circling a collection of objects in a tree using xymatrix

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