diff --git a/vertex_cover/src/main.rs b/vertex_cover/src/main.rs
index fc75d3c..42b2e7f 100644
--- a/vertex_cover/src/main.rs
+++ b/vertex_cover/src/main.rs
@@ -155,8 +155,11 @@ enum Method {
 #[derive(Debug, Parser)]
 struct Args {
     filename: PathBuf,
+    #[clap(default_value = "reduction2")]
     method: Method,
     k: Option<u16>,
+    #[clap(short, long)]
+    reverse: bool,
 }
 
 fn main() {
@@ -169,6 +172,20 @@ fn main() {
         let r = vertex_cover(&graph, k, args.method);
         eprintln!("{}: {:?}", k, start.elapsed());
         r
+    } else if args.reverse {
+        let mut k = graph.num_vertices();
+        let mut last_solution = None;
+        loop {
+            let start = std::time::Instant::now();
+            let r = vertex_cover(&graph, k, args.method);
+            eprintln!("{}: {:?}", k, start.elapsed());
+            if let Some(r) = r {
+                k = r.len() as u16 - 1;
+                last_solution = Some(r);
+            } else {
+                break last_solution;
+            };
+        }
     } else {
         let mut k = 0;
         loop {
diff --git a/vertex_cover/src/owned.rs b/vertex_cover/src/owned.rs
index 1171e0c..3dc3d31 100644
--- a/vertex_cover/src/owned.rs
+++ b/vertex_cover/src/owned.rs
@@ -237,6 +237,8 @@ pub fn reduction2(graph: &mut Graph, k: u16) -> Option<Vec<u16>> {
         let _ = graph.reinsert_vertices(1);
 
         r
+    } else if graph.is_empty() {
+        Some(Vec::new())
     } else if k == 0 {
         if graph.is_empty() {
             Some(Vec::new())
@@ -343,6 +345,10 @@ pub fn reduction2(graph: &mut Graph, k: u16) -> Option<Vec<u16>> {
             }
         }
     } else if let Some(vertex) = graph.get_vertex_with_degree_greater(3) {
+        if k < 1 {
+            return None;
+        }
+
         graph.remove_vertex(vertex);
 
         match reduction2(graph, k - 1) {
@@ -374,6 +380,6 @@ pub fn reduction2(graph: &mut Graph, k: u16) -> Option<Vec<u16>> {
             }
         }
     } else {
-        unreachable!()
+        unreachable!("{k}")
     }
 }