Add is_bipartite(::Graph)

docs/src/Combinatorics/graphs.md

@@ -71,6 +71,7 @@ shortest_path_dijkstra
 signed_incidence_matrix(g::Graph)
 is_isomorphic(g1::Graph{T}, g2::Graph{T}) where {T <: Union{Directed, Undirected}}
 is_isomorphic_with_permutation(G1::Graph, G2::Graph)
+is_bipartite(g::Graph{Undirected})
 ```
 
 ### Edges

src/Combinatorics/Graphs/functions.jl

@@ -1339,3 +1339,20 @@ function laplacian_matrix(g::Graph)
   A = matrix(ZZ, adjacency_matrix(g))
   return D-A
 end
+
+@doc raw"""
+    is_bipartite(g::Graph{Undirected})
+
+Returns true if the undirected graph `g` is bipartite.
+
+# Examples
+```jldoctest
+julia> g = graph_from_edges([[1,2],[2,3],[3,4]]);
+
+julia> is_bipartite(g)
+true
+```
+"""
+function is_bipartite(g::Graph{Undirected})
+  return Polymake.graph.Graph{Undirected}(ADJACENCY=pm_object(g)).BIPARTITE::Bool
+end

src/exports.jl

@@ -814,6 +814,7 @@ export is_bicoset
 export is_bijective
 export is_binary
 export is_binomial
+export is_bipartite
 export is_bounded
 export is_canonically_isomorphic
 export is_canonically_isomorphic_with_map

test/Combinatorics/Graph.jl

@@ -190,4 +190,15 @@
       @test matrix(ZZ, adjacency_matrix(G1)) == matrix(ZZ, [0 1 1 0; 1 0 0 1; 1 0 0 1; 0 1 1 0])
       @test laplacian_matrix(G1) == matrix(ZZ, [2 -1 -1 0; -1 2 0 -1; -1 0 2 -1; 0 -1 -1 2])
     end
+
+    @testset "is_bipartite" begin
+      G0 = Graph{Undirected}(3)
+      add_edge!(G0,1,2)
+      add_edge!(G0,1,3)
+      add_edge!(G0,2,3)
+      @test is_bipartite(G0) == false
+
+      G1 = graph_from_edges([[1,2],[2,3],[3,4]])
+      @test is_bipartite(G1) == true
+    end
 end