diff --git a/lib/possible_bipartition.rb b/lib/possible_bipartition.rb
index 69507f1..e34b464 100644
--- a/lib/possible_bipartition.rb
+++ b/lib/possible_bipartition.rb
@@ -1,4 +1,36 @@
 
+# Time complexity: O(V + E), where V is the number of vertices and E is the number of adjecent neighbors. 
+# Space complexity: O(V) where v is the number of vertices/dogs because of the dog_group array. The recursive stack will be at most O(n), as well. 
 def possible_bipartition(dislikes)
-  raise NotImplementedError, "possible_bipartition isn't implemented yet"
+  # 0 is no color
+  # 1 is one color
+  # -1 is the other
+
+
+  # keep track of the colors
+  # if a color exists for one, we return false?
+  dog_group = Array.new(dislikes.length, 0)
+  p dislikes
+  dislikes.length.times do |dog|
+    if dog_group[dog] == 0 && !dfs(dislikes, dog_group, dog, 1)
+      return false
+    end
+  end
+  return true
+end
+
+def dfs(dislikes, dog_group, current_dog, group)
+
+  dog_group[current_dog] = group
+
+  dislikes[current_dog].each do |disliked_dog|
+    if dog_group[disliked_dog] == group
+      return false
+    end
+
+    if dog_group[disliked_dog] == 0 && !dfs(dislikes, dog_group, disliked_dog, group * -1)
+      return false
+    end
+  end
+  return true
 end