Fix variant hints in path errors and IsomorphicSpanningTree complexity

problemreductions-cli/src/commands/graph.rs

@@ -375,6 +375,24 @@ pub(crate) fn variant_to_full_slash(variant: &BTreeMap<String, String>) -> Strin
     }
 }
 
+/// Build a hint string listing available variants for a problem name.
+/// Returns an empty string if there is only one variant (nothing to disambiguate).
+pub(crate) fn variant_hint_for(graph: &ReductionGraph, name: &str) -> String {
+    let variants = graph.variants_for(name);
+    if variants.len() <= 1 {
+        return String::new();
+    }
+    let list: Vec<String> = variants
+        .iter()
+        .map(|v| format!("{}{}", name, variant_to_full_slash(v)))
+        .collect();
+    format!(
+        "\nTip: try specifying a variant. Available variants for {}:\n  {}\n",
+        name,
+        list.join(", "),
+    )
+}
+
 /// Format a problem node as **bold name/variant** in slash notation.
 /// This is the single source of truth for "name/variant" display.
 fn fmt_node(_graph: &ReductionGraph, name: &str, variant: &BTreeMap<String, String>) -> String {
@@ -550,8 +568,10 @@ pub fn path(
             out.emit_with_default_name("", &text, &json)
         }
         None => {
+            let variant_hint = variant_hint_for(&graph, &dst_spec.name);
             anyhow::bail!(
-                "No reduction path from {} to {}\n\n\
+                "No reduction path from {} to {}\n\
+                 {variant_hint}\n\
                  Usage: pred path <SOURCE> <TARGET>\n\
                  Example: pred path MIS QUBO\n\n\
                  Run `pred show {}` and `pred show {}` to check available reductions.",
@@ -578,8 +598,10 @@ fn path_all(
         graph.find_paths_up_to(src_name, src_variant, dst_name, dst_variant, max_paths + 1);
 
     if all_paths.is_empty() {
+        let variant_hint = variant_hint_for(graph, dst_name);
         anyhow::bail!(
-            "No reduction path from {} to {}\n\n\
+            "No reduction path from {} to {}\n\
+             {variant_hint}\n\
              Usage: pred path <SOURCE> <TARGET> --all\n\
              Example: pred path MIS QUBO --all\n\n\
              Run `pred show {}` and `pred show {}` to check available reductions.",

problemreductions-cli/src/commands/reduce.rs

@@ -125,8 +125,10 @@ pub fn reduce(
         );
 
         best_path.ok_or_else(|| {
+            let variant_hint = variant_hint_for(&graph, &dst_ref.name);
             anyhow::anyhow!(
-                "No witness-capable reduction path from {} to {}\n\n\
+                "No witness-capable reduction path from {} to {}\n\
+                 {variant_hint}\n\
                  Hint: generate a path file first, then pass it with --via:\n\
                    pred path {} {} -o path.json\n\
                    pred reduce {} --via path.json -o reduced.json",
@@ -196,4 +198,4 @@ pub fn reduce(
     Ok(())
 }
 
-use super::graph::variant_to_full_slash;
+use super::graph::{variant_hint_for, variant_to_full_slash};

src/models/graph/isomorphic_spanning_tree.rs

@@ -195,7 +195,7 @@ pub(crate) fn canonical_model_example_specs() -> Vec<crate::example_db::specs::M
 }
 
 crate::declare_variants! {
-    default IsomorphicSpanningTree<SimpleGraph> => "num_vertices^num_vertices",
+    default IsomorphicSpanningTree<SimpleGraph> => "2^num_vertices",
 }
 
 #[cfg(test)]