# Vertical line in binomial tree is ruining node coloring

How do I stop the dummy nodes from being colored?

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{matrix,fit,backgrounds,calc}

\begin{document}

\begin{tikzpicture}[>=stealth,sloped]
\matrix (tree) [%
matrix of nodes,
minimum size=1cm,
column sep=2.5cm,
row sep=0.4cm,
column 2/.style={nodes={draw,fill=green!30,rounded corners}},
column 3/.style={nodes={draw,fill=red!30,rounded corners}},
]
{
& |(top-left)|       & |(top-right)|       &  $_0 S_T$             \\
&                    &  $_0S_{2\Delta t}$  &                  \\
& $_0S_{\Delta t}$   &                     &  $_1 S_T$             \\
$_0S_0$ &                    &  $_1S_{2\Delta t}$  &                  \\
& $_1S_{\Delta t}$   &                     &  $_2 S_T$         \\
&                    &  $_2S_{2\Delta t}$  &                \\
& |(bottom-left)|    & |(bottom-right)|    &  $_3 S_T$    \\
};

\draw[->] (tree-4-1) -- (tree-3-2) node [midway,above] {$p$};
\draw[->] (tree-4-1) -- (tree-5-2) node [midway,below] {$1-p$};
\draw[->] (tree-3-2) -- (tree-2-3) node [midway,above] {};
\draw[->] (tree-3-2) -- (tree-4-3) node [midway,below] {};
\draw[->] (tree-5-2) -- (tree-4-3) node [midway,above] {};
\draw[->] (tree-5-2) -- (tree-6-3) node [midway,below] {};

\draw[->] (tree-2-3) -- (tree-1-4) node [midway,above] {};
\draw[->] (tree-2-3) -- (tree-3-4) node [midway,below] {};
\draw[->] (tree-4-3) -- (tree-3-4) node [midway,above] {};
\draw[->] (tree-4-3) -- (tree-5-4) node [midway,below] {};
\draw[->] (tree-6-3) -- (tree-5-4) node [midway,above] {};
\draw[->] (tree-6-3) -- (tree-7-4) node [midway,below] {};

% t-line
\draw[dashed] ($(top-left.north)!.5!(top-right.north)$) -- ($(bottom-left.south)!.5!(bottom-right.south)$);
\node at ($(bottom-left.south)!.5!(bottom-right.south)-(0,1em)$) {$\tau$};

\end{tikzpicture}

\end{document}

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You can use draw=none and fill=none. Here I put both in a style called dummy:

## Code

 \matrix (tree) [%
matrix of nodes,
minimum size=1cm,
column sep=2.5cm,
row sep=0.4cm,
column 2/.style={nodes={draw,fill=green!30,rounded corners}},
column 3/.style={nodes={draw,fill=red!30,rounded corners}},
dummy/.style={fill=none,draw=none}
]
{
& |[dummy](top-left)|       & |[dummy](top-right)|       &  $_0 S_T$             \\
&                    &  $_0S_{2\Delta t}$  &                  \\
& $_0S_{\Delta t}$   &                     &  $_1 S_T$             \\
$_0S_0$ &                    &  $_1S_{2\Delta t}$  &                  \\
& $_1S_{\Delta t}$   &                     &  $_2 S_T$         \\
&                    &  $_2S_{2\Delta t}$  &                \\
& |[dummy](bottom-left)|    & |[dummy](bottom-right)|    &  $_3 S_T$    \\
};


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