Considering the following MWE:
\documentclass[fleqn,xcolor={dvipsnames,table}]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathtools, nccmath, textcomp} % https://tex.stackexchange.com/questions/155534/how-to-reduce-the-size-of-fractions-typed-in-align-environment
\usepackage{booktabs} %https://tex.stackexchange.com/a/112514/166831
\usepackage{array}
\let\tc\textcolor
\definecolor{darkgreen}{rgb}{0.09, 0.45, 0.27}
\definecolor{dauphineblue}{rgb}{0.19,0.267,0.5176}
\newcommand{\tdb}[1]{\tc{dauphineblue}{#1}}
\newcommand{\tdr}[1]{\tc{darkred}{#1}}
% Thème CambridgeUS
\usetheme{CambridgeUS}
\usepackage{amsmath}
\makeatletter
\newcommand{\srcsize}{@setfontsize{\srcsize}{7pt}{7pt}}
\makeatother
\begin{document}
\begingroup
\srcsize %https://tex.stackexchange.com/a/207655/166831
\begin{frame}
Min $\sum_{i\in V} \text{some minimizing function with terms} + x + y$
\begin{alignat*}{2}
\displaystyle\sum_{\substack{i\in V\\j\dots}} \tdr{x_{ij}} + \sum_{\substack{i\in V\\j\dots}} \tdr{x_{ij}} &= c \tdr{x_{ij}} ,&\quad\tdr{\forall i \in V}\\
\dots \text{some more constraints}\\
\displaystyle\sum_{\substack{i\in V\\j\dots}}\sum_{\substack{i\in V\\j\dots}} \tdr{x_{ij}} &\ge 3 + \tc{darkgreen}{\sigma} &\\
\tc{darkgreen}{\sigma}~ & \ge \tdr{x_{ij}} ,&\quad \tdr{\forall i \in V} \\
\displaystyle\sum_{\substack{i\in V\\j\dots}} \tdb{y_{ij}} + \displaystyle\sum_{\substack{i\in V\\j\dots}} \tdb{y_{ij}} &= (1-\tdr{x_{ij}}),&\quad \tdb{\forall i \in V}\\
\tdb{y_{ij}}&\le \tdr{y_{jj}}, &\quad \tdb{\forall (i,j) \in V}\\
\tc{darkgreen}{\sigma}~ & \in \mathbb N &\\
\tdr{y_{11}} &= 1&\\
\tdr{x_{ij}} &\in \mathbb B ,\quad&\tc{darkgreen}{\forall (i,j) \in V^2, i < j}\\
\tdb{y_{ij}} &\in \mathbb B ,\quad&\tc{darkgreen}{\forall (i,j) \in V^2}\\
\tdb{z_{ij}} &\in \mathbb B ,\quad&\tc{darkgreen}{\forall (i,j) \in V^2, i < j}
\end{alignat*}
\end{frame}
\endgroup
\begingroup
\srcsize %https://tex.stackexchange.com/a/207655/166831
\begin{frame}
Min $\sum_{i\in V} \text{some minimizing function with terms} + x + y$
\[\left.\begin{array}{rrr}
\displaystyle\sum_{\substack{i\in V\\j\dots}} \tdr{x_{ij}} + \sum_{\substack{i\in V\\j\dots}} \tdr{x_{ij}} &= c \tdr{x_{ij}} ,&\quad\tdr{\forall i \in V}\\
\dots \text{some more constraints}\\
\displaystyle\sum_{\substack{i\in V\\j\dots}}\sum_{\substack{i\in V\\j\dots}} \tdr{x_{ij}} &\ge 3 + \tc{darkgreen}{\sigma} &\\
\tc{darkgreen}{\sigma}~ & \ge \tdr{x_{ij}} ,&\quad \tdr{\forall i \in V} \\
\displaystyle\sum_{\substack{i\in V\\j\dots}} \tdb{y_{ij}} + \displaystyle\sum_{\substack{i\in V\\j\dots}} \tdb{y_{ij}} &= (1-\tdr{x_{ij}}),&\quad \tdb{\forall i \in V}
\end{array}\color{darkred}\right\}\text{\tdr{Ring constraints}}\]
\[\left.\begin{array}{rrr}
\displaystyle\sum_{\substack{i\in V\\j\dots}} \tdb{y_{ij}} + \displaystyle\sum_{\substack{i\in V\\j\dots}} \tdb{y_{ij}} &= (1-\tdr{x_{ij}}),&\quad \tdb{\forall i \in V}\\
\tdb{y_{ij}}&\le \tdr{y_{jj}}, &\quad \tdb{\forall (i,j) \in V}\\
\tc{darkgreen}{\sigma}~ & \in \mathbb N &\\
\tdr{y_{11}} &= 1&
\end{array}\color{dauphineblue}\right\}\text{\tdb{Star constraints}}\]
\begin{alignat*}{2}
\tc{darkgreen}{\sigma}~ & \in \mathbb N &\\
\tdr{x_{ij}} &\in \mathbb B ,\quad&\tc{darkgreen}{\forall (i,j) \in V^2, i < j}\\
\tdb{y_{ij}} &\in \mathbb B ,\quad&\tc{darkgreen}{\forall (i,j) \in V^2}\\
\tdb{z_{ij}} &\in \mathbb B ,\quad&\tc{darkgreen}{\forall (i,j) \in V^, i < j}
\end{alignat*}
\end{frame}
\endgroup
\end{document}
It produces:
Then I want to add two right brackets as follows on the next frame:
My problem is that I didn't succeed to have the same alignment thanks to & for the equations. The \le, \ge, =, \in signs are not aligned anymore nor the indices domains \forall. I also want that my two brackets to be vertically exactly one above each other and not having the red one on the right. Thank you for your help :D
