diff --git a/src/uu/tsort/src/tsort.rs b/src/uu/tsort/src/tsort.rs
index 9b60e4828..2f0b4c9b8 100644
--- a/src/uu/tsort/src/tsort.rs
+++ b/src/uu/tsort/src/tsort.rs
@@ -2,7 +2,7 @@
 //
 // For the full copyright and license information, please view the LICENSE
 // file that was distributed with this source code.
-//spell-checker:ignore TAOCP
+//spell-checker:ignore TAOCP indegree
 use clap::{crate_version, Arg, Command};
 use std::collections::{HashMap, HashSet, VecDeque};
 use std::fmt::Display;
@@ -75,7 +75,7 @@ pub fn uumain(args: impl uucore::Args) -> UResult<()> {
     };
 
     // Create the directed graph from pairs of tokens in the input data.
-    let mut g = Graph::default();
+    let mut g = Graph::new(input.clone());
     for ab in data.split_whitespace().collect::<Vec<&str>>().chunks(2) {
         match ab {
             [a, b] => g.add_edge(a, b),
@@ -83,20 +83,8 @@ pub fn uumain(args: impl uucore::Args) -> UResult<()> {
         }
     }
 
-    match g.run_tsort() {
-        Err(cycle) => {
-            show!(TsortError::Loop(input.to_string()));
-            for node in &cycle {
-                show!(TsortError::LoopNode(node.to_string()));
-            }
-            println!("{}", cycle.join("\n"));
-            Ok(())
-        }
-        Ok(ordering) => {
-            println!("{}", ordering.join("\n"));
-            Ok(())
-        }
-    }
+    g.run_tsort();
+    Ok(())
 }
 pub fn uu_app() -> Command {
     Command::new(uucore::util_name())
@@ -112,6 +100,20 @@ pub fn uu_app() -> Command {
         )
 }
 
+/// Find the element `x` in `vec` and remove it, returning its index.
+fn remove<T>(vec: &mut Vec<T>, x: T) -> Option<usize>
+where
+    T: PartialEq,
+{
+    for i in 0..vec.len() {
+        if vec[i] == x {
+            vec.remove(i);
+            return Some(i);
+        }
+    }
+    None
+}
+
 // We use String as a representation of node here
 // but using integer may improve performance.
 #[derive(Default)]
@@ -125,12 +127,20 @@ impl<'input> Node<'input> {
         self.successor_names.push(successor_name);
     }
 }
-#[derive(Default)]
+
 struct Graph<'input> {
+    name: String,
     nodes: HashMap<&'input str, Node<'input>>,
 }
 
 impl<'input> Graph<'input> {
+    fn new(name: String) -> Graph<'input> {
+        Self {
+            name,
+            nodes: HashMap::default(),
+        }
+    }
+
     fn add_node(&mut self, name: &'input str) {
         self.nodes.entry(name).or_default();
     }
@@ -147,9 +157,14 @@ impl<'input> Graph<'input> {
             to_node.predecessor_count += 1;
         }
     }
+
+    fn remove_edge(&mut self, u: &'input str, v: &'input str) {
+        remove(&mut self.nodes.get_mut(u).unwrap().successor_names, v);
+        self.nodes.get_mut(v).unwrap().predecessor_count -= 1;
+    }
+
     /// Implementation of algorithm T from TAOCP (Don. Knuth), vol. 1.
-    fn run_tsort(&mut self) -> Result<Vec<&'input str>, Vec<&'input str>> {
-        let mut result = Vec::with_capacity(self.nodes.len());
+    fn run_tsort(&mut self) {
         // First, we find a node that have no prerequisites (independent nodes)
         // If no such node exists, then there is a cycle.
         let mut independent_nodes_queue: VecDeque<&'input str> = self
@@ -166,10 +181,18 @@ impl<'input> Graph<'input> {
         independent_nodes_queue.make_contiguous().sort_unstable(); // to make sure the resulting ordering is deterministic we need to order independent nodes
                                                                    // FIXME: this doesn't comply entirely with the GNU coreutils implementation.
 
-        // we remove each independent node, from the graph, updating each successor predecessor_count variable as we do.
-        while let Some(name_of_next_node_to_process) = independent_nodes_queue.pop_front() {
-            result.push(name_of_next_node_to_process);
-            if let Some(node_to_process) = self.nodes.remove(name_of_next_node_to_process) {
+        // To make sure the resulting ordering is deterministic we
+        // need to order independent nodes.
+        //
+        // FIXME: this doesn't comply entirely with the GNU coreutils
+        // implementation.
+        independent_nodes_queue.make_contiguous().sort_unstable();
+
+        while !self.nodes.is_empty() {
+            // Get the next node (breaking any cycles necessary to do so).
+            let v = self.find_next_node(&mut independent_nodes_queue);
+            println!("{v}");
+            if let Some(node_to_process) = self.nodes.remove(v) {
                 for successor_name in node_to_process.successor_names {
                     let successor_node = self.nodes.get_mut(successor_name).unwrap();
                     successor_node.predecessor_count -= 1;
@@ -180,20 +203,61 @@ impl<'input> Graph<'input> {
                 }
             }
         }
+    }
 
-        // if the graph has no cycle (it's a dependency tree), the graph should be empty now, as all nodes have been deleted.
-        if self.nodes.is_empty() {
-            Ok(result)
-        } else {
-            // otherwise, we detect and show a cycle to the user (as the GNU coreutils implementation does)
-            Err(self.detect_cycle())
+    /// Get the in-degree of the node with the given name.
+    fn indegree(&self, name: &str) -> Option<usize> {
+        self.nodes.get(name).map(|data| data.predecessor_count)
+    }
+
+    // Pre-condition: self.nodes is non-empty.
+    fn find_next_node(&mut self, frontier: &mut VecDeque<&'input str>) -> &'input str {
+        // If there are no nodes of in-degree zero but there are still
+        // un-visited nodes in the graph, then there must be a cycle.
+        // We need to find the cycle, display it, and then break the
+        // cycle.
+        //
+        // A cycle is guaranteed to be of length at least two. We break
+        // the cycle by deleting an arbitrary edge (the first). That is
+        // not necessarily the optimal thing, but it should be enough to
+        // continue making progress in the graph traversal.
+        //
+        // It is possible that deleting the edge does not actually
+        // result in the target node having in-degree zero, so we repeat
+        // the process until such a node appears.
+        loop {
+            match frontier.pop_front() {
+                None => self.find_and_break_cycle(frontier),
+                Some(v) => return v,
+            }
+        }
+    }
+
+    fn find_and_break_cycle(&mut self, frontier: &mut VecDeque<&'input str>) {
+        let cycle = self.detect_cycle();
+        show!(TsortError::Loop(self.name.clone()));
+        for node in &cycle {
+            show!(TsortError::LoopNode(node.to_string()));
+        }
+        let u = cycle[0];
+        let v = cycle[1];
+        self.remove_edge(u, v);
+        if self.indegree(v).unwrap() == 0 {
+            frontier.push_back(v);
         }
     }
 
     fn detect_cycle(&self) -> Vec<&'input str> {
+        // Sort the nodes just to make this function deterministic.
+        let mut nodes = Vec::new();
+        for node in self.nodes.keys() {
+            nodes.push(node);
+        }
+        nodes.sort_unstable();
+
         let mut visited = HashSet::new();
         let mut stack = Vec::with_capacity(self.nodes.len());
-        for &node in self.nodes.keys() {
+        for node in nodes {
             if !visited.contains(node) && self.dfs(node, &mut visited, &mut stack) {
                 return stack;
             }
diff --git a/tests/by-util/test_tsort.rs b/tests/by-util/test_tsort.rs
index f86add294..299a8f0bb 100644
--- a/tests/by-util/test_tsort.rs
+++ b/tests/by-util/test_tsort.rs
@@ -83,3 +83,31 @@ fn test_split_on_any_whitespace() {
         .succeeds()
         .stdout_only("a\nb\n");
 }
+
+#[test]
+fn test_cycle() {
+    // The graph looks like:  a --> b <==> c --> d
+    new_ucmd!()
+        .pipe_in("a b b c c d c b")
+        .fails()
+        .code_is(1)
+        .stdout_is("a\nc\nd\nb\n")
+        .stderr_is("tsort: -: input contains a loop:\ntsort: b\ntsort: c\n");
+}
+
+#[test]
+fn test_two_cycles() {
+    // The graph looks like:
+    //
+    //        a
+    //        |
+    //        V
+    // c <==> b <==> d
+    //
+    new_ucmd!()
+        .pipe_in("a b b c c b b d d b")
+        .fails()
+        .code_is(1)
+        .stdout_is("a\nc\nd\nb\n")
+        .stderr_is("tsort: -: input contains a loop:\ntsort: b\ntsort: c\ntsort: -: input contains a loop:\ntsort: b\ntsort: d\n");
+}