The Size of the Giant Joint Component in a Binomial Random Double Graph

We study the joint components in a random 'double graph' that is obtained by superposing red and blue binomial graphs on $n$~vertices. A component maximal set of vertices supports both spanning tree. show there are critical pairs edge densities at which giant appears. In contrast to standard graph model, phase transition first order: size largest jumps from $O(1)$ $\Theta(n)$ point. connect this phenomenon properties certain bicoloured branching process.