diff -up src/sage/graphs/graph_decompositions/cutwidth.pyx.orig src/sage/graphs/graph_decompositions/cutwidth.pyx
--- src/sage/graphs/graph_decompositions/cutwidth.pyx.orig	2022-01-30 06:41:50.000000000 -0700
+++ src/sage/graphs/graph_decompositions/cutwidth.pyx	2022-03-06 17:04:36.234711622 -0700
@@ -522,12 +522,12 @@ def cutwidth_dyn(G, lower_bound=0):
                 if exists(g, neighborhoods, 0, 0, i, k) <= k:
                     order = find_order(g, neighborhoods, k)
                     return k, [g.int_to_vertices[i] for i in order]
+
+        order = find_order(g, neighborhoods, k)
+        return k, [g.int_to_vertices[i] for i in order]
     finally:
         sig_free(neighborhoods)
 
-    order = find_order(g, neighborhoods, k)
-    return k, [g.int_to_vertices[i] for i in order]
-
 cdef inline int exists(FastDigraph g, uint8_t* neighborhoods, int S, int cost_S, int v, int k):
     r"""
     Check whether an ordering with the given cost `k` exists, and updates data