From 9e3e525a5b3d5481377f40a052ce56739b2af02c Mon Sep 17 00:00:00 2001 From: didericis Date: Fri, 24 Apr 2026 21:10:06 -0400 Subject: [PATCH] Replace plane_depth_labelling with plane_depth_sequencing paper and script, remove unused lib modules Co-Authored-By: Claude Sonnet 4.6 --- lib/dual_graph.py | 29 --- lib/edge_for_dual_edge.py | 12 -- lib/edge_graph.py | 42 ----- lib/tait_coloring.py | 18 -- lib/vertex_coloring.py | 11 -- papers/plane_depth_labelling/paper.aux | 7 - .../plane_depth_labelling/paper.fdb_latexmk | 46 ----- papers/plane_depth_labelling/paper.fls | 145 --------------- papers/plane_depth_labelling/paper.log | 149 ---------------- papers/plane_depth_labelling/paper.pdf | Bin 53379 -> 0 bytes papers/plane_depth_labelling/paper.synctex.gz | Bin 985 -> 0 bytes papers/plane_depth_labelling/paper.tex | 83 --------- papers/plane_depth_sequencing/paper.aux | 8 + .../plane_depth_sequencing/paper.fdb_latexmk | 54 ++++++ papers/plane_depth_sequencing/paper.fls | 75 ++++++++ papers/plane_depth_sequencing/paper.log | 168 ++++++++++++++++++ papers/plane_depth_sequencing/paper.pdf | Bin 0 -> 142375 bytes .../plane_depth_sequencing/paper.synctex.gz | Bin 0 -> 11781 bytes papers/plane_depth_sequencing/paper.tex | 119 +++++++++++++ plane_depth_sequencing.py | 65 +++++++ 20 files changed, 489 insertions(+), 542 deletions(-) delete mode 100644 lib/dual_graph.py delete mode 100644 lib/edge_for_dual_edge.py delete mode 100644 lib/edge_graph.py delete mode 100644 lib/tait_coloring.py delete mode 100644 lib/vertex_coloring.py delete mode 100644 papers/plane_depth_labelling/paper.aux delete mode 100644 papers/plane_depth_labelling/paper.fdb_latexmk delete mode 100644 papers/plane_depth_labelling/paper.fls delete mode 100644 papers/plane_depth_labelling/paper.log delete mode 100644 papers/plane_depth_labelling/paper.pdf delete mode 100644 papers/plane_depth_labelling/paper.synctex.gz delete mode 100644 papers/plane_depth_labelling/paper.tex create mode 100644 papers/plane_depth_sequencing/paper.aux create mode 100644 papers/plane_depth_sequencing/paper.fdb_latexmk create mode 100644 papers/plane_depth_sequencing/paper.fls create mode 100644 papers/plane_depth_sequencing/paper.log create mode 100644 papers/plane_depth_sequencing/paper.pdf create mode 100644 papers/plane_depth_sequencing/paper.synctex.gz create mode 100644 papers/plane_depth_sequencing/paper.tex create mode 100644 plane_depth_sequencing.py diff --git a/lib/dual_graph.py b/lib/dual_graph.py deleted file mode 100644 index 6d2c97e..0000000 --- a/lib/dual_graph.py +++ /dev/null @@ -1,29 +0,0 @@ -"""Utilities for working with planar dual graphs.""" -from typing import Any -from sage.all import Graph - - -def find_vertex_for_dual_face(dual_face: Any) -> Any | None: - """Return the primal vertex shared by all faces in the dual face, or None.""" - shared_vertices = None - for dual_edge in dual_face: - vertices = set(map(lambda e: e[0], dual_edge[0])) - if shared_vertices: - shared_vertices.intersection_update(vertices) - else: - shared_vertices = vertices - if len(shared_vertices) == 1: - return shared_vertices.pop() - return None - - -def _dual_edge_has_vertex(dual_edge: Any, vertex: Any) -> bool: - return any(vertex in edge for dual_vertex in dual_edge for edge in dual_vertex) - - -def find_dual_face_for_removed_vertex(planar_dual: Graph, vertex: Any) -> Any | None: - """Return the dual face of length 5 whose every dual edge contains the given vertex.""" - for dual_face in list[Any](planar_dual.faces()): # type: ignore[call-arg] - if len(dual_face) == 5 and all(_dual_edge_has_vertex(de, vertex) for de in dual_face): - return dual_face - return None diff --git a/lib/edge_for_dual_edge.py b/lib/edge_for_dual_edge.py deleted file mode 100644 index 6d1c27c..0000000 --- a/lib/edge_for_dual_edge.py +++ /dev/null @@ -1,12 +0,0 @@ -"""Utilities for finding primal edges corresponding to dual edges.""" -from typing import Any, cast - -def get_edge_for_dual_edge(dual_edge: Any) -> tuple[int, int, None]: - """Return the primal edge shared by both faces of the given dual edge.""" - edges: list[set[Any]] = [] - for e in (dual_edge[0] + dual_edge[1]): - edge = set(e) - if edge in edges: - return cast(tuple[int, int, None], e) - edges.append(edge) - raise ValueError(f"Error finding edge for {dual_edge}") diff --git a/lib/edge_graph.py b/lib/edge_graph.py deleted file mode 100644 index 383f0ea..0000000 --- a/lib/edge_graph.py +++ /dev/null @@ -1,42 +0,0 @@ -"""Utilities for constructing edge graphs from planar graphs.""" -from typing import Any, cast -from sage.all import Graph - - -def get_edge_graph_pos(edge_graph: Graph, pos_src: dict[Any, Any]) -> dict[Any, tuple[Any, Any]]: - """Return a position dict for edge graph vertices, using midpoints of the source positions.""" - pos: dict[Any, tuple[Any, Any]] = {} - for e in cast(list[Any], edge_graph.vertices()): # type: ignore - pos[e] = ( - (pos_src[e[0]][0] + pos_src[e[1]][0]) / 2, - (pos_src[e[0]][1] + pos_src[e[1]][1]) / 2 - ) - return pos - - -def get_edge_graph(graph: Graph, set_pos: bool = True) -> Graph: - """Return the edge graph of the given graph, optionally setting vertex positions.""" - pos_src: dict[Any, Any] | None = None - pos: dict[Any, tuple[Any, Any]] = {} - if set_pos: - pos_src = cast(dict[Any, Any], graph.get_pos()) # type: ignore - - g = Graph() - for e in cast(list[Any], graph.edges()): # type: ignore - g.add_vertex(e) # type: ignore - if pos_src: - pos[e] = ( - (pos_src[e[0]][0] + pos_src[e[1]][0]) / 2, - (pos_src[e[0]][1] + pos_src[e[1]][1]) / 2 - ) - - for v in cast(list[Any], graph.vertices()): # type: ignore - incident_edges = cast(list[Any], graph.edges_incident(v)) # type: ignore - if len(incident_edges) == 1: - continue - for i, e1 in enumerate(incident_edges): - e2 = incident_edges[(i + 1) % len(incident_edges)] - g.add_edge(e1, e2) # type: ignore - if set_pos: - g.set_pos(pos) # type: ignore - return g diff --git a/lib/tait_coloring.py b/lib/tait_coloring.py deleted file mode 100644 index 92251b7..0000000 --- a/lib/tait_coloring.py +++ /dev/null @@ -1,18 +0,0 @@ -"""Utilities for computing Tait colorings from vertex colorings of the dual graph.""" -from typing import Any, cast -from sage.all import Graph -from lib.edge_for_dual_edge import get_edge_for_dual_edge - -def get_tait_coloring(planar_dual: Graph, coloring: dict[Any, int]) -> dict[Any, int]: - """Return a Tait (edge 3-coloring) from a vertex 4-coloring of the dual graph.""" - tait_coloring: dict[Any, int] = {} - for dual_edge in cast(list[Any], planar_dual.edges()): # type: ignore - edge = get_edge_for_dual_edge(dual_edge) - colors = {coloring[edge[0]], coloring[edge[1]]} - if colors in ({0, 1}, {2, 3}): - tait_coloring[dual_edge] = 0 - elif colors in ({1, 2}, {0, 3}): - tait_coloring[dual_edge] = 1 - else: - tait_coloring[dual_edge] = 2 - return tait_coloring diff --git a/lib/vertex_coloring.py b/lib/vertex_coloring.py deleted file mode 100644 index 586296d..0000000 --- a/lib/vertex_coloring.py +++ /dev/null @@ -1,11 +0,0 @@ -"""Utilities for verifying vertex colorings.""" -from typing import Any, cast -from sage.all import Graph - -def check_vertex_coloring(graph: Graph, vertex_coloring: dict[Any, int]) -> bool: - """Raise ValueError if any two adjacent vertices share a color.""" - for v in cast(list[Any], graph.vertices()): # type: ignore - for nv in cast(list[Any], graph.neighbors(v)): # type: ignore - if vertex_coloring[nv] == vertex_coloring[v]: - raise ValueError(f"Color {nv} equal to color {v}") - return True diff --git a/papers/plane_depth_labelling/paper.aux b/papers/plane_depth_labelling/paper.aux deleted file mode 100644 index 05a181d..0000000 --- a/papers/plane_depth_labelling/paper.aux +++ /dev/null @@ -1,7 +0,0 @@ -\relax -\newlabel{tocindent-1}{0pt} -\newlabel{tocindent0}{0pt} -\newlabel{tocindent1}{0pt} -\newlabel{tocindent2}{0pt} -\newlabel{tocindent3}{0pt} -\gdef \@abspage@last{1} diff 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1 for v, d in distances if v != source} + + +def deep_embedding(g: Graph, outer_cycle: list[Any], plane_depth_labelling: dict[Any, int] | None = None) -> Graph: + """ + Return the deep embedding of g relative to outer_cycle. + + For every interior triangular face whose three vertices all have the same + plane depth, a new vertex is added adjacent to each vertex of that face. + """ + if plane_depth_labelling is None: + plane_depth_labelling = get_plane_depth_labelling(g, outer_cycle) + outer_vertices = set(outer_cycle) + + embedding = g.get_embedding() + if embedding is None: + g.is_planar(set_embedding=True) + embedding = g.get_embedding() + + g_prime = g.copy() + new_vertex = max(g.vertices()) + 1 + + for face in g.faces(embedding): + face_vertices = [u for u, v in face] + if set(face_vertices) == outer_vertices: + continue + if plane_depth_labelling[face_vertices[0]] == plane_depth_labelling[face_vertices[1]] == plane_depth_labelling[face_vertices[2]]: + g_prime.add_vertex(new_vertex) + g_prime.add_edges([(new_vertex, v) for v in face_vertices]) + new_vertex += 1 + + return g_prime + + +def generate_example(n: int) -> DeeplyEmbeddedGraph: + """Generate a random maximal planar graph of size n and return the triangulation, outer cycle, and deep embedding.""" + g = graphs.RandomTriangulation(n) + g.is_planar(set_embedding=True) + embedding = g.get_embedding() + faces = g.faces(embedding) + outer_cycle = [u for u, v in random.choice(faces)] + plane_depth_labelling = get_plane_depth_labelling(g, outer_cycle) + return DeeplyEmbeddedGraph(graph=g, outer_cycle=outer_cycle, plane_depth_labelling=plane_depth_labelling, deep_embedding=deep_embedding(g, outer_cycle, plane_depth_labelling))