diff --git a/Cargo.lock b/Cargo.lock
index 0f63664..4bdbbda 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -68,6 +68,12 @@ version = "0.2.155"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "97b3888a4aecf77e811145cadf6eef5901f4782c53886191b2f693f24761847c"
 
+[[package]]
+name = "log"
+version = "0.4.21"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "90ed8c1e510134f979dbc4f070f87d4313098b704861a105fe34231c70a3901c"
+
 [[package]]
 name = "petgraph"
 version = "0.6.5"
@@ -124,6 +130,7 @@ name = "treewidth-heuristic-using-clique-graphs"
 version = "0.1.0"
 dependencies = [
  "itertools",
+ "log",
  "petgraph",
  "rand",
  "rustc-hash",
diff --git a/Cargo.toml b/Cargo.toml
index b7d58a5..deee918 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -11,4 +11,5 @@ repository = "https://github.com/RaoulLuque/treewidth-heuristic-clique-graph"
 petgraph = "0.6.4"
 itertools = "0.13"
 rand = "0.8.5"
-rustc-hash = { version ="2.0.0", git = "https://github.com/rust-lang/rustc-hash"}
\ No newline at end of file
+rustc-hash = { version ="2.0.0", git = "https://github.com/rust-lang/rustc-hash"}
+log = "0.4.21"
\ No newline at end of file
diff --git a/src/compute_treewidth_upper_bound.rs b/src/compute_treewidth_upper_bound.rs
index cb8117a..cfd78dc 100644
--- a/src/compute_treewidth_upper_bound.rs
+++ b/src/compute_treewidth_upper_bound.rs
@@ -43,14 +43,14 @@ pub enum SpanningTreeConstructionMethod {
 /// a tree decomposition.
 ///
 /// See [TreewidthComputationMethod] for the different options of spanning tree construction.
-/// 
+///
 /// Also see [edge weight functions][crate::clique_graph_edge_weight_functions] for the different
 /// weight options for the edges in the clique graph.
 ///
-/// It is possible to not use the clique graph but the clique graph with a bound on the 
+/// It is possible to not use the clique graph but the clique graph with a bound on the
 /// size of the cliques instead. The resulting graph is the intersection graph of the set of all
 /// cliques that are maximal or have a size of clique_bound
-/// 
+///
 /// Can also check the tree decomposition for correctness after computation which will up to double
 /// the running time. If so, will panic if the tree decomposition if incorrect returning the vertices
 /// and path that is faulty.
@@ -79,7 +79,7 @@ pub fn compute_treewidth_upper_bound<
             // .sorted()
             .collect()
     } else {
-        find_maximum_cliques::<Vec<_>, _, S>(graph)
+        find_maximal_cliques::<Vec<_>, _, S>(graph)
             // .sorted()
             .collect()
     };
diff --git a/src/fill_bags_while_generating_mst.rs b/src/fill_bags_while_generating_mst.rs
index 3953856..57d8fd9 100644
--- a/src/fill_bags_while_generating_mst.rs
+++ b/src/fill_bags_while_generating_mst.rs
@@ -3,8 +3,15 @@ use std::{
     hash::BuildHasher,
 };
 
+use log::trace;
 use petgraph::{graph::NodeIndex, Graph, Undirected};
 
+/// The function computes a [tree decomposition][https://en.wikipedia.org/wiki/Tree_decomposition]
+/// with the vertices having bags (HashSets) as labels
+/// given a clique graph. For this a minimum spanning tree of the clique graph is constructed using
+/// prim's algorithm and the edge labels in the clique graph as edge weights. Whenever a new vertex
+/// is added to the spanning tree, the bags of the current spanning tree are filled up/updated
+/// according to the [tree decomposition criteria][https://en.wikipedia.org/wiki/Tree_decomposition#Definition].
 pub fn fill_bags_while_generating_mst<N, E, O: Ord, S: Default + BuildHasher + Clone>(
     clique_graph: &Graph<HashSet<NodeIndex, S>, O, Undirected>,
     edge_weight_heuristic: fn(&HashSet<NodeIndex, S>, &HashSet<NodeIndex, S>) -> O,
@@ -44,7 +51,7 @@ pub fn fill_bags_while_generating_mst<N, E, O: Ord, S: Default + BuildHasher + C
     while !clique_graph_remaining_vertices.is_empty() {
         // DEBUG
         if clique_graph_remaining_vertices.len() % 30 == 0 {
-            println!(
+            trace!(
                 "{} vertices remaining",
                 clique_graph_remaining_vertices.len()
             );
@@ -179,6 +186,11 @@ fn fill_bags<O, S: BuildHasher>(
     }
 }
 
+/// Computes a tree decomposition similar to [fill_bags_while_generating_mst] except that whenever
+/// a vertex is added to the current spanning tree and the bags of the current spanning tree are
+/// filled up/updated, edges to other vertices in the entire clique graph are updated (in order to
+/// preserve the property that two vertices/bags in the clique graph are adjacent iff they have a
+/// non-empty intersection).
 pub fn fill_bags_while_generating_mst_update_edges<
     N,
     E,
@@ -315,7 +327,7 @@ fn fill_bags_from_result_graph_updating_edges<S: BuildHasher + Clone, O>(
     }
 }
 
-/// Adapted from fill_bags
+/// Adapted from [fill_bags]
 fn fill_bags_updating_edges<O, S: BuildHasher>(
     start_vertex: NodeIndex,
     end_vertex: NodeIndex,
@@ -493,6 +505,10 @@ pub fn fill_bags_while_generating_mst_using_tree<N, E, O: Ord, S: Default + Buil
     result_graph
 }
 
+/// Computes a tree decomposition similar to [fill_bags_while_generating_mst] except that instead of
+/// using edge weights in prim's algorithm, the weight of an edge (u,v) (v is not yet in the
+/// spanning tree) is the size of the biggest bag in the spanning tree if v was added to the
+/// spanning tree and the bags were filled up/updated accordingly.
 pub fn fill_bags_while_generating_mst_least_bag_size<
     N,
     E,
diff --git a/src/find_maximum_cliques.rs b/src/find_maximum_cliques.rs
index f3bd3f5..038d43e 100644
--- a/src/find_maximum_cliques.rs
+++ b/src/find_maximum_cliques.rs
@@ -4,10 +4,11 @@ use std::hash::BuildHasher;
 use std::iter::from_fn;
 use std::{collections::HashSet, hash::Hash};
 
-/// Returns an iterator that produces all maximum cliques in the given graph in arbitrary order.
+/// Returns an iterator that produces all [maximal cliques][https://en.wikipedia.org/wiki/Clique_(graph_theory)#Definitions]
+/// in the given graph in arbitrary order.
 ///
-/// This algorithm is adapted from <https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.clique.find_cliques.html>.
-pub fn find_maximum_cliques<TargetColl, G, S: Default + BuildHasher + Clone>(
+/// This algorithm is adapted from [networkX find_cliques algorithm][https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.clique.find_cliques.html].
+pub fn find_maximal_cliques<TargetColl, G, S: Default + BuildHasher + Clone>(
     graph: G,
 ) -> impl Iterator<Item = TargetColl>
 where
@@ -110,8 +111,8 @@ where
     })
 }
 
-/// Returns an iterator that produces all maximum cliques with maximum size k or cliques that are
-/// part of maximum cliques that are themselves bigger in size than k in arbitrary order.
+/// Returns an iterator that produces (once each) all cliques that are [maximal][https://en.wikipedia.org/wiki/Clique_(graph_theory)#Definitions]
+/// (and of size less than k) or of size k (and not necessarily maximal) in arbitrary order.
 ///
 /// Uses the [find_maximum_cliques] method.
 pub fn find_maximum_cliques_bounded<TargetColl, G, S: Default + Clone + BuildHasher>(
@@ -126,7 +127,7 @@ where
     TargetColl: FromIterator<G::NodeId>,
     <G as GraphBase>::NodeId: 'static,
 {
-    let mut maximum_cliques = find_maximum_cliques::<HashSet<_, S>, G, S>(graph);
+    let mut maximum_cliques = find_maximal_cliques::<HashSet<_, S>, G, S>(graph);
     let mut combinations = HashSet::<_, S>::default().into_iter().combinations(k);
     let mut seen_combinations = HashSet::<_, S>::default();
     from_fn(move || loop {
@@ -160,7 +161,7 @@ mod tests {
             let test_graph = crate::tests::setup_test_graph(i);
 
             let mut cliques: Vec<Vec<_>> =
-                find_maximum_cliques::<Vec<_>, _, RandomState>(&test_graph.graph).collect();
+                find_maximal_cliques::<Vec<_>, _, RandomState>(&test_graph.graph).collect();
 
             for i in 0..cliques.len() {
                 cliques[i].sort();
diff --git a/src/generate_partial_k_tree.rs b/src/generate_partial_k_tree.rs
index 0a8c2da..ec8dda3 100644
--- a/src/generate_partial_k_tree.rs
+++ b/src/generate_partial_k_tree.rs
@@ -4,17 +4,18 @@ use rand::{seq::IteratorRandom, Rng};
 
 use crate::maximum_minimum_degree_plus;
 
-/// Generates a [k-tree](https://en.wikipedia.org/wiki/K-tree) and then randomly removes p percent of the edges
-/// to get a [partial k-tree](https://en.wikipedia.org/wiki/Partial_k-tree). To guarantee a treewidth of k,
-/// this procedure is repeated until the treewidth of the graph is at least k according to the minimum
-/// maximum degree heuristic.
+/// Generates a [k-tree](https://en.wikipedia.org/wiki/K-tree) and then randomly removes p percent
+/// of the edges to get a [partial k-tree](https://en.wikipedia.org/wiki/Partial_k-tree). To
+/// guarantee a treewidth of k, this procedure is repeated until the treewidth of the graph is at
+/// least k according to the minimum maximum degree heuristic.
 ///
-/// **Caution!**: Due to the randomness involved, this function could in theory take indefinitely to generate
-/// a partial k-tree with the wished treewidth.
+/// **Caution!**: Due to the randomness involved, this function could in theory take
+/// indefinitely to generate a partial k-tree with the desired treewidth.
 ///
-/// If p > 100 all edges will be removed. The Rng is passed in to increase performance when calling the function multiple times in a row.
+/// If p > 100 all edges will be removed. The Rng is passed in to increase performance when
+/// calling the function multiple times in a row.
 ///
-/// Returns None if k > n
+/// Returns None if k > n.
 pub fn generate_partial_k_tree_with_guaranteed_treewidth(
     k: usize,
     n: usize,
@@ -37,10 +38,10 @@ pub fn generate_partial_k_tree_with_guaranteed_treewidth(
 /// If p > 100 all edges will be removed. The Rng is passed in to increase performance when calling
 /// the function multiple times in a row.
 ///
-/// Returns None if k > n
+/// Returns None if k > n.
 ///
-/// The number of edges in a k_tree are k * (k - 1) / 2 + k * (n - k). So the number of removed edges in a
-/// partial_k_tree will be (k * (k - 1) / 2 + k * (n - k)) * p / 100 rounded down
+/// The number of edges in a k_tree are k * (k - 1) / 2 + k * (n - k). So the number of removed
+/// edges in a partial_k_tree will be (k * (k - 1) / 2 + k * (n - k)) * p / 100 rounded down.
 pub fn generate_partial_k_tree(
     k: usize,
     n: usize,
@@ -67,7 +68,7 @@ pub fn generate_partial_k_tree(
 }
 
 /// Generates a [k-tree](https://en.wikipedia.org/wiki/K-tree) with n vertices and k in the definition.
-/// Returns None if k > n
+/// Returns None if k > n.
 pub fn generate_k_tree(k: usize, n: usize) -> Option<Graph<i32, i32, Undirected>> {
     if k > n {
         None
diff --git a/src/lib.rs b/src/lib.rs
index b5c474b..bcddec5 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -26,7 +26,7 @@ pub(crate) use fill_bags_while_generating_mst::{
     fill_bags_while_generating_mst_update_edges, fill_bags_while_generating_mst_using_tree,
 };
 pub(crate) use find_connected_components::find_connected_components;
-pub(crate) use find_maximum_cliques::{find_maximum_cliques, find_maximum_cliques_bounded};
+pub(crate) use find_maximum_cliques::{find_maximal_cliques, find_maximum_cliques_bounded};
 pub(crate) use find_width_of_tree_decomposition::find_width_of_tree_decomposition;
 pub use generate_partial_k_tree::{
     generate_k_tree, generate_partial_k_tree, generate_partial_k_tree_with_guaranteed_treewidth,