Add min-degree-5 conjecture and computational verification search

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

plane_diamond_coloring.py

@@ -81,6 +81,26 @@ def search_counterexample_comprehensive(max_order: int, min_order: int = 4) -> l
     return counterexamples
 
 
+def search_min_degree_counterexample_comprehensive(max_order: int, minimum_degree: int, min_order: int = 4) -> list[Graph]:
+    """
+    Iterate through every maximal planar graph of order in [min_order, max_order]
+    with the given minimum degree, and return all those without a plane diamond
+    coloring.
+    """
+    counterexamples: list[Graph] = []
+    for n in range(min_order, max_order + 1):
+        checked = 0
+        for g in graphs.planar_graphs(n, minimum_connectivity=3, maximum_face_size=3, minimum_degree=minimum_degree):
+            checked += 1
+            if not has_plane_diamond_coloring(g):
+                print(f"Counterexample at order {n}, min_degree {minimum_degree} (graph #{checked}): {g.graph6_string()}")
+                counterexamples.append(g)
+            if checked % 100 == 0:
+                print(f"  order {n}: checked {checked} graphs, {len(counterexamples)} counterexamples so far")
+        print(f"order {n} done: {checked} triangulations of min degree {minimum_degree} checked")
+    return counterexamples
+
+
 if __name__ == "__main__":
     import sys
     if len(sys.argv) > 1 and sys.argv[1] == "comprehensive":
@@ -90,6 +110,14 @@ if __name__ == "__main__":
         print(f"Found {len(counterexamples)} counterexamples in orders {min_order}..{max_order}")
         for g in counterexamples:
             canonize_and_save_graph(g)
+    elif len(sys.argv) > 1 and sys.argv[1] == "min-degree":
+        max_order = int(sys.argv[2]) if len(sys.argv) > 2 else 13
+        minimum_degree = int(sys.argv[3]) if len(sys.argv) > 3 else 5
+        min_order = int(sys.argv[4]) if len(sys.argv) > 4 else 4
+        counterexamples = search_min_degree_counterexample_comprehensive(max_order, minimum_degree, min_order)
+        print(f"Found {len(counterexamples)} counterexamples in orders {min_order}..{max_order} with min degree {minimum_degree}")
+        for g in counterexamples:
+            canonize_and_save_graph(g)
     else:
         n = int(sys.argv[1]) if len(sys.argv) > 1 else 12
         num_trials = int(sys.argv[2]) if len(sys.argv) > 2 else 100