Added forest cover function

src/traversals/dfs.jl

@@ -25,3 +25,32 @@ end
 function dfs_parents(graph::AbstractNamedGraph, vertex; kwargs...)
   return _dfs_parents(graph, vertex; kwargs...)
 end
+
+#Given a graph, split it into its connected components, construct a spanning tree over each of them
+# and take the union (adding in edges between the trees to recover a connected graph)
+function spanning_forest(g::AbstractNamedGraph)
+  components = connected_components(g)
+  return reduce(
+    union,
+    NamedGraph[
+      undirected_graph(bfs_tree(g[g_comp], first(g_comp))) for g_comp in components
+    ],
+  )
+end
+
+#Given a graph g with vertex set V, build a set of forests (each with vertex set V) which covers all edges in g
+# (see https://en.wikipedia.org/wiki/Arboricity) We do not find the minimum but our tests show this algorithm performs well
+function build_forest_cover(g::AbstractNamedGraph)
+  edges_collected = edgetype(g)[]
+  remaining_edges = edges(g)
+  forests = NamedGraph[]
+  while !isempty(remaining_edges)
+    g_reduced = rem_edges(g, edges_collected)
+    g_reduced_spanning_forest = spanning_forest(g_reduced)
+    push!(edges_collected, edges(g_reduced_spanning_forest)...)
+    push!(forests, g_reduced_spanning_forest)
+    setdiff!(remaining_edges, edges(g_reduced_spanning_forest))
+  end
+
+  return forests
+end

test/test_forests.jl

@@ -0,0 +1,30 @@
+using Test
+using Graphs
+using NamedGraphs
+using NamedGraphs:
+  decorate_graph_edges,
+  decorate_graph_vertices,
+  hexagonal_lattice_graph,
+  triangular_lattice_graph,
+  build_forest_cover
+
+@testset "Test Forest Cover" begin
+  gs = [
+    named_grid((6, 1)),
+    named_grid((3, 3, 3)),
+    hexagonal_lattice_graph(6, 6),
+    named_comb_tree((4, 4)),
+    named_grid((10, 10)),
+    triangular_lattice_graph(5, 5; periodic=true),
+  ]
+  for g in gs
+    forest_cover = build_forest_cover(g)
+    cover_edges = reduce(vcat, edges.(forest_cover))
+    @test issetequal(cover_edges, edges(g))
+    for f in forest_cover
+      trees = NamedGraph[f[vs] for vs in connected_components(f)]
+      @test all(is_tree.(trees))
+      @test issetequal(vertices(f), vertices(g))
+    end
+  end
+end

test/test_namedgraphgenerators.jl

@@ -30,7 +30,6 @@ using Random
   @test dims[1] > dims[2]
 
   g = triangular_lattice_graph(2, 1)
-  @show g
   dims = maximum(vertices(g))
   @test dims[1] > dims[2]