Handle compound medial tires in cut labelling

papers/medial_tire_cuts/lib/medial_tire_cut_labelling.py

@@ -205,7 +205,8 @@ def label_and_cut(graph: FullMedialTireGraph, entry_edge: int,
 
 
 def up_apex_cuts(graph: FullMedialTireGraph, entry_edge: int,
-                 bij: Mapping[str, object] | None = None) -> dict[int, object]:
+                 bij: Mapping[str, object] | None = None,
+                 shared_apexes: set[object] | None = None) -> dict[int, object]:
     """Up-tooth apex cuts prescribed after the walk-depth traversal.
 
     The returned dict maps each cut up-tooth edge to the apex vertex to
@@ -218,11 +219,12 @@ def up_apex_cuts(graph: FullMedialTireGraph, entry_edge: int,
         i: (bij[f"u{i}"] if bij is not None else graph.apex_of_edge(i))
         for i in graph.up_edges
     }
+    shared_apexes = shared_apexes or set()
     multiplicity = Counter(apex_by_edge.values())
     return {
         i: apex
         for i, apex in apex_by_edge.items()
-        if i != entry_edge and multiplicity[apex] == 1
+        if i != entry_edge and multiplicity[apex] == 1 and apex not in shared_apexes
     }