diff --git a/src/coloring.jl b/src/coloring.jl
index cf3d8f79..84007d56 100644
--- a/src/coloring.jl
+++ b/src/coloring.jl
@@ -422,9 +422,23 @@ Encode a set of 2-colored trees resulting from the [`acyclic_coloring`](@ref) al
 $TYPEDFIELDS
 """
 struct TreeSet{T}
+    """
+    For a tree index `1 <= k <= nt`, the list
+    `list = reverse_bfs_order[tree_edge_indices[k]:(tree_edge_indices[k+1]-1)]` is a list of edges
+    `list[i] = (leaf, inner)` of the `k`th tree such that `leaf` is a leaf of the tree containing
+    the edges `list[i:end]`.
+    From an other point of view, `reverse(list)` contains the edges in the order of a breadth first
+    (BFS) traversal order of the `k`th tree starting from a depth-minimizing root.
+    """
     reverse_bfs_orders::Vector{Tuple{T,T}}
+    "For a tree index `1 <= k <= nt`, `is_star[k]` indicates whether the `k`th three is a star."
     is_star::Vector{Bool}
+    """
+    `tree_edge_indices[1]` is one and `tree_edge_indices[k+1] - tree_edge_indices[k]` is the number of edges in the `k`th tree.
+    One can think of it as a kind of fused vector of offsets (similar to the `colptr` field of `SparseMatrixCSC`) of all trees together.
+    """
     tree_edge_indices::Vector{T}
+    "numbers of 2-colored trees for which trees sharing the same 2 colors have disjoint edges"
     nt::T
 end
 
@@ -432,6 +446,7 @@ function TreeSet(
     g::AdjacencyGraph{T},
     forest::Forest{T},
     buffer::AbstractVector{T},
+    # The value of `reverse_bfs_orders` is ignored, we just provide the storage for it (or reuse memory allocated during acyclic coloring)
     reverse_bfs_orders::Vector{Tuple{T,T}},
     ne::Integer,
 ) where {T}
@@ -566,7 +581,15 @@ function TreeSet(
     # Number of edges treated
     num_edges_treated = zero(T)
 
-    # reverse_bfs_orders contains the reverse breadth first (BFS) traversal order for each tree in the forest
+    # The `rank` of the `k`th tree encoded in `forest` does not correspond
+    # to the depth of the tree rooted as the root encoded in `forest` because
+    # `forest.parents[u] = v` only needs a path to exists from `u` to `v` but
+    # there may not be an edge `(u, v)`.
+    # We also want a root `r` that minimizes the depth of the tree rooted at
+    # `r`. To achieve this, we start from each leaf and remove the corresponding
+    # edges. We then look at all leaves of the corresponding graphs and repeat
+    # the process until there is only one vertex left. This vertex will then be
+    # a depth-minimizing root.
     for k in 1:nt
         # Initialize the queue to store the leaves
         queue_start = 1