The Red and Blue Friends

The Map of the Empire

The Map of the Empire

In Sheldor's empire, there are several villages connected by roads of different length. The map of the empire is shown below.

However, because the emperor cannot put up with the high costs of maintaining so many roads decided that he would only keep as many roads as to keep the whole kingdom connected but the total length of the roads is minimum. He would blow up all the other roads.

The direct road between \(\color{red}{\text{Red}}\) and \(\color{blue}{\text{Blue}}\) is the shortest road in the empire. Will this road still be kept in this regime?

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