Add branching medial tire decomposition example

papers/medial_tire_decompositions_of_plane_triangulations/experiments/branching_medial_tire_decomposition/random_c5_n30_medial_tire_decomposition_1.md

@@ -0,0 +1,19 @@
+# Random medial tire decomposition 1
+
+- vertices: 30
+- edges: 84
+- node connectivity: 5
+- source vertex: 14
+- tire-tree nodes: 4
+- tire-tree edges: 3
+
+| node | depth | faces | annular | up | down | bites | full medial tires |
+|--:|--:|--:|--:|--:|--:|--:|--:|
+| T0 | 2 | 23 | 23 | 10 | 13 | 0 | 1 |
+| T0.0 |  |  | | 10 | 13 | - | `UDDUDUUDDUDUDUDUDDDUUDD` |
+| T1 | 1 | 15 | 15 | 5 | 10 | 0 | 1 |
+| T1.0 |  |  | | 5 | 10 | - | `UDDDUDDUDUDDDUD` |
+| T2 | 3 | 8 | 5 | 11 | 0 | 0 | 1 |
+| T2.0 |  |  | | 5 | 0 | - | `UUUUU` |
+| T3 | 3 | 5 | 5 | 5 | 0 | 0 | 1 |
+| T3.0 |  |  | | 5 | 0 | - | `UUUUU` |

papers/medial_tire_decompositions_of_plane_triangulations/experiments/draw_random_medial_tire_decompositions.py

@@ -450,10 +450,18 @@ def draw_case(out_dir: Path, graph_idx: int, g: nx.Graph, source: int):
 def run(args: argparse.Namespace):
     out_dir = Path(args.out_dir)
     out_dir.mkdir(parents=True, exist_ok=True)
+
+    if args.graph6:
+        graphs = [nx.from_graph6_bytes(args.graph6.encode())]
+        if args.source is None:
+            raise ValueError("--source is required with --graph6")
+        sources = [args.source]
+    else:
         graphs = sample_plantri_graphs(args.n, args.count, args.seed, args.scan_limit)
         rng = random.Random(args.seed + 101)
-    for i, graph in enumerate(graphs, start=1):
-        source = rng.choice(list(graph.nodes()))
+        sources = [rng.choice(list(graph.nodes())) for graph in graphs]
+
+    for i, (graph, source) in enumerate(zip(graphs, sources), start=1):
         png, pdf, node_count, tire_count = draw_case(out_dir, i, graph, source)
         print(
             f"case {i}: source={source}, connectivity={nx.node_connectivity(graph)}, "
@@ -469,6 +477,8 @@ def main():
     parser.add_argument("--count", type=int, default=2)
     parser.add_argument("--seed", type=int, default=20260615)
     parser.add_argument("--scan-limit", type=int, default=500)
+    parser.add_argument("--graph6", help="draw this graph6 graph instead of sampling")
+    parser.add_argument("--source", type=int, help="source vertex for --graph6")
     parser.add_argument(
         "--out-dir",
         default=str(PAPER_DIR / "experiments" / "random_medial_tire_decompositions"),