diff --git a/src/lib.rs b/src/lib.rs
index 08939e9..9891a0e 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -57,8 +57,7 @@ impl LinkCutTree {
         if !matches!(self.forest[v].parent, Parent::Root) || v == w {
             return; // already connected
         }
-        // assert_eq!(self.forest[v].left, None);
-        self.forest[v].left = Some(w);
+        self.forest[v].left = Some(w); // v is the root of its represented tree, so no need to check if it has a left child
         self.forest[w].parent = Parent::Node(v);
     }
 
diff --git a/tests/test_connectivity.rs b/tests/test_connectivity.rs
index 0467283..e15967e 100644
--- a/tests/test_connectivity.rs
+++ b/tests/test_connectivity.rs
@@ -68,14 +68,14 @@ enum Operation {
 }
 
 #[test]
-pub fn test_connectivity() {
+pub fn connectivity() {
     let mut rng = create_random_generator();
     let edges = create_random_tree(&mut rng);
 
     // initialize link-cut tree, we start with a forest of single nodes
     // (edges are not added yet):
     let mut lctree = LinkCutTree::new(NUMBER_OF_NODES);
-    let mut edges_in_tree = HashSet::new();
+    let mut edges_in_forest = HashSet::new();
     let mut component_ids = (0..NUMBER_OF_NODES).collect::<Vec<usize>>();
 
     // perform random operations: link, cut, or connected:
@@ -87,19 +87,19 @@ pub fn test_connectivity() {
                 println!("Link {} {}", v, w);
                 lctree.link(*v, *w);
 
-                edges_in_tree.insert((*v, *w));
-                component_ids = connected_components(&edges_in_tree);
+                edges_in_forest.insert((*v, *w));
+                component_ids = connected_components(&edges_in_forest);
             }
             Operation::Cut => {
-                if edges_in_tree.is_empty() {
+                if edges_in_forest.is_empty() {
                     continue;
                 }
-                let (v, w) = edges_in_tree.iter().choose(&mut rng).unwrap();
+                let (v, w) = edges_in_forest.iter().choose(&mut rng).unwrap();
                 println!("Cut {} {}", v, w);
                 lctree.cut(*v);
 
-                edges_in_tree.remove(&(*v, *w));
-                component_ids = connected_components(&edges_in_tree);
+                edges_in_forest.remove(&(*v, *w));
+                component_ids = connected_components(&edges_in_forest);
             }
             Operation::Connected => {
                 let v = rng.gen_range(0..NUMBER_OF_NODES);