diff --git a/python/cudf_polars/cudf_polars/experimental/parallel.py b/python/cudf_polars/cudf_polars/experimental/parallel.py
index a783f91fc73..8d08fbd0166 100644
--- a/python/cudf_polars/cudf_polars/experimental/parallel.py
+++ b/python/cudf_polars/cudf_polars/experimental/parallel.py
@@ -60,8 +60,7 @@ def _lower_ir_single(
     partition_info = reduce(operator.or_, _partition_info)
 
     # Check that child partitioning is supported
-    count = max(partition_info[c].count for c in children)
-    if count > 1:
+    if any(partition_info[c].count > 1 for c in children):
         raise NotImplementedError(
             f"Class {type(ir)} does not support multiple partitions."
         )  # pragma: no cover
@@ -276,7 +275,7 @@ def _(
         return rec.state["default_mapper"](ir)  # pragma: no cover
 
     # Lower children
-    children, _partition_info = zip(*(rec(c) for c in ir.children), strict=False)
+    children, _partition_info = zip(*(rec(c) for c in ir.children), strict=True)
     partition_info = reduce(operator.or_, _partition_info)
 
     # Partition count is the sum of all child partitions
@@ -294,11 +293,12 @@ def _(
 ) -> MutableMapping[Any, Any]:
     part_out = 0
     key_name = get_key_name(ir)
-    graph: MutableMapping[Any, Any] = {}
-    for child in ir.children:
-        for i in range(partition_info[child].count):
-            graph[(key_name, part_out)] = (get_key_name(child), i)
-            part_out += 1
+    partition = itertools.count()
+    graph = {
+        (key_name, next(partition)): (get_key_name(child), i)
+        for i in range(partition_info[child].count)
+        for child in ir.children
+    }
     return graph