Consider an undirected connected graph $G$ where each of its edges e has cost c$($e$).$ Recall the following definitions

A cut $S$ of $G$ is a subset of its vertices.

The cutset of $S$ is the set of edges of $G$ with one endpoint in $S$ and one endpoint outside S$.$

Blue Rule: find a cut of $G$ whose cutset $D$ does not contain a blue edge. Color the minimum cost uncolored edge in $D$ blue.

Apply the Blue Rule to $G$ until it can no longer be applied to color an uncolored edge blue. Select the correct statement below.

Every node of $G$ is an endpoint of some blue edge.

If the subgraph $T$ of $G$ of all blue edges is a spanning tree and $e$ is any edge of $G$ not in $T,$ then e costs more than any edge in $T.$

The subgraph of $G$ of all blue edges may be disconnected.

There may be a cycle of blue edges in G$.$