diff --git a/src/traversals/bipartition.jl b/src/traversals/bipartition.jl
index 1d1310c18..955b8c21c 100644
--- a/src/traversals/bipartition.jl
+++ b/src/traversals/bipartition.jl
@@ -12,9 +12,9 @@ An empty graph will return an empty vector but is bipartite.
 function bipartite_map(g::AbstractGraph{T}) where T
     nvg = nv(g)
     if !is_directed(g)
-        ccs = filter(x -> length(x) > 2, connected_components(g))
+        ccs = filter(x -> length(x) >= 2, connected_components(g))
     else
-        ccs = filter(x -> length(x) > 2, weakly_connected_components(g))
+        ccs = filter(x -> length(x) >= 2, weakly_connected_components(g))
     end
     seen = zeros(Bool, nvg)
     colors = zeros(Bool, nvg)
diff --git a/test/traversals/bipartition.jl b/test/traversals/bipartition.jl
index 31736078a..c8d390fa7 100644
--- a/test/traversals/bipartition.jl
+++ b/test/traversals/bipartition.jl
@@ -21,9 +21,29 @@
     g10 = CompleteBipartiteGraph(10, 10)
     for g in testgraphs(g10)
         T = eltype(g)
-        @test @inferred(bipartite_map(g10)) == Vector{T}([ones(T, 10); 2 * ones(T, 10)])
+        @test @inferred(bipartite_map(g)) == Vector{T}([ones(T, 10); 2 * ones(T, 10)])
 
         h = blkdiag(g, g)
         @test @inferred(bipartite_map(h)) == Vector{T}([ones(T, 10); 2 * ones(T, 10); ones(T, 10); 2 * ones(T, 10)])
     end
+
+    g2 = CompleteGraph(2)
+    for g in testgraphs(g2)
+        @test @inferred(bipartite_map(g)) == Vector{eltype(g)}([1, 2])
+    end
+
+    g2 = Graph(2)
+    for g in testgraphs(g2)
+        @test @inferred(bipartite_map(g)) == Vector{eltype(g)}([1, 1])
+    end
+
+    g2 = DiGraph(2)
+    for g in testdigraphs(g2)
+        @test @inferred(bipartite_map(g)) == Vector{eltype(g)}([1, 1])
+    end
+
+    g2 = PathDiGraph(2)
+    for g in testdigraphs(g2)
+        @test @inferred(bipartite_map(g)) == Vector{eltype(g)}([1, 2])
+    end
 end