diff --git a/model_compression_toolkit/core/common/graph/memory_graph/cut.py b/model_compression_toolkit/core/common/graph/memory_graph/cut.py
index bd21f502b..8d4b5bae8 100644
--- a/model_compression_toolkit/core/common/graph/memory_graph/cut.py
+++ b/model_compression_toolkit/core/common/graph/memory_graph/cut.py
@@ -12,28 +12,36 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 # ==============================================================================
+from dataclasses import dataclass, field
+
 from typing import List, Set
 
 from model_compression_toolkit.core.common import BaseNode
 from model_compression_toolkit.core.common.graph.memory_graph.memory_element import MemoryElements
 
 
+@dataclass(frozen=True)
 class Cut:
     """
     A Cut object that contains a set of ordered nodes and their memory elements.
-    """
 
-    def __init__(self, op_order: List[BaseNode], op_record: Set[BaseNode], mem_elements: MemoryElements):
-        """
-        Args:
-            op_order: A list of the cut's nodes (model layers), ordered by their addition to the cut (first-to-last).
-            op_record: A (unordered) set of the nodes in the cut.
-            mem_elements: MemoryElements object which represents the activation tensors of the cut's nodes.
-        """
-
-        self.op_order = op_order
-        self.op_record = op_record
-        self.mem_elements = mem_elements
+    Args:
+        op_order: A list of the cut's nodes (model layers), ordered by their addition to the cut (first-to-last).
+        op_record: A (unordered) set of the nodes in the cut.
+        mem_elements: MemoryElements object which represents the activation tensors of the cut's nodes.
+    """
+    op_order: List[BaseNode]
+    op_record: Set[BaseNode]
+    mem_elements: MemoryElements
+
+    _sorted_elements_signature: str = field(init=False, default=None)
+
+    @property
+    def sorted_elements_signature(self):
+        if self._sorted_elements_signature is None:
+            object.__setattr__(self, '_sorted_elements_signature',
+                               '_'.join(sorted([e.node_name for e in self.mem_elements.elements])))
+        return self._sorted_elements_signature
 
     def memory_size(self) -> float:
         """
diff --git a/model_compression_toolkit/core/common/graph/memory_graph/max_cut_astar.py b/model_compression_toolkit/core/common/graph/memory_graph/max_cut_astar.py
index 2c121fd4c..a346c0043 100644
--- a/model_compression_toolkit/core/common/graph/memory_graph/max_cut_astar.py
+++ b/model_compression_toolkit/core/common/graph/memory_graph/max_cut_astar.py
@@ -232,7 +232,8 @@ def _get_cut_to_expand(self, open_list: Set[Cut], costs: Dict[Cut, float], route
         max_cut_len = max([len(routes[c]) for c in open_list])
         ordered_cuts_list = sorted(open_list,
                                    key=lambda c: (self.accumulate(costs[c], self.estimate(c, estimate)),
-                                                  max_cut_len - len(routes[c])))
+                                                  max_cut_len - len(routes[c]),
+                                                  c.sorted_elements_signature))
 
         assert len(ordered_cuts_list) > 0
         return ordered_cuts_list[0]
diff --git a/tests/keras_tests/function_tests/test_graph_max_cut.py b/tests/keras_tests/function_tests/test_graph_max_cut.py
index 780b2e3b4..e8a49a8a5 100644
--- a/tests/keras_tests/function_tests/test_graph_max_cut.py
+++ b/tests/keras_tests/function_tests/test_graph_max_cut.py
@@ -139,3 +139,17 @@ def test_graph_max_cut_plain_graph_real_model(self):
         self.assertIsNotNone(cuts)
         self.assertTrue(len(cuts) > 0)
         self.assertTrue(max_cut_size >= memory_graph.memory_lbound_single_op)
+
+    def test_graph_max_cut_deterministic_order(self):
+        input_shape = (8, 8, 3)
+        model = complex_model(input_shape)
+        graph = model_reader(model)
+
+        solutions = [compute_graph_max_cut(MemoryGraph(graph)) for _ in range(10)]
+
+        schedules, max_cut_sizes, cuts_solutions = zip(*solutions)
+        assert len(set(max_cut_sizes)) == 1
+        # nodes within each cut can be in different order, and cuts can be in different order inside cuts list,
+        # but overall the cuts should be identical between different runs
+        sorted_cuts_solutions = [sorted(cut.sorted_elements_signature for cut in cuts) for cuts in cuts_solutions]
+        assert all(cuts == sorted_cuts_solutions[0] for cuts in sorted_cuts_solutions[1:])