diff --git a/edmonds.cpp b/edmonds.cpp
index 227c8ce..3449fa2 100644
--- a/edmonds.cpp
+++ b/edmonds.cpp
@@ -1,8 +1,76 @@
 #include "edmonds.h"
 
-namespace Edmonds {
-ED::Graph maximum_matching(ED::Graph & graph)
-{
+using namespace ED;
 
+namespace Edmonds {
+
+std::vector<NodeId> path_to_forest_root(Graph const & graph, NodeId id)
+{
+   std::vector<NodeId> retval;
+   retval.push_back(id);
+   while (graph.matched_neighbor(id) != id)
+   {
+      id = graph.matched_neighbor(id);
+      retval.push_back(id);
+
+      // Note that it is guaranteed that this does not produce a loop:
+      // We are traversing the path to a root of the forest,
+      // but we know that each root is exposed by M, so after traversing
+      // the matching edge, we cannot have reached a root.
+      id = graph.ear_or_root_neighbor(id);
+      retval.push_back(id);
+   }
+   return retval;
+}
+
+
+Graph maximum_matching(Graph & graph)
+{
+   graph.reset_forest();
+   for(NodeId id = 0; id < graph.num_nodes(); ++id) {
+      if (graph.is_out_of_forest(id))
+      {
+         for(NodeId neighbor_id : graph.node(id).neighbors())
+         {
+            if (graph.is_out_of_forest(neighbor_id))
+            {
+               // Grow Forest
+               graph.node(neighbor_id).ear_or_root_neighbor = id;
+            }
+            else if (graph.is_outer(neighbor_id) and \
+               graph.root_of_ear_component(id) != graph.root_of_ear_component(neighbor_id))
+            {
+               std::vector<NodeId> x_path = path_to_forest_root(graph, id);
+               std::vector<NodeId> y_path = path_to_forest_root(graph, neighbor_id);
+
+               if (x_path.back() != y_path.back())
+               {
+                  // Paths are disjoint -> augment
+                  graph.node(x_path.front()).matched_neighbor = y_path.front();
+                  graph.node(y_path.front()).matched_neighbor = x_path.front();
+
+                  // TODO: put this into own method?
+                  for(size_t i = 1; i < x_path.size(); i += 2)
+                  {
+                     graph.node(x_path[i]).matched_neighbor = x_path[i+1];
+                     graph.node(x_path[i+1]).matched_neighbor = x_path[i];
+                  }
+                  for(size_t i = 1; i < y_path.size(); i += 2)
+                  {
+                     graph.node(y_path[i]).matched_neighbor = y_path[i+1];
+                     graph.node(y_path[i+1]).matched_neighbor = y_path[i];
+                  }
+                  // Note that since this is tail-recursion, this will not generate
+                  // new stack frames in OPT mode
+                  return maximum_matching(graph);
+               }
+               else
+               {
+                  // Paths are not disjoint -> shrink blossom
+               }
+            }
+         }
+      }
+   }
 };
 }
\ No newline at end of file
diff --git a/graph.hpp b/graph.hpp
index 16ccd00..5622327 100644
--- a/graph.hpp
+++ b/graph.hpp
@@ -146,6 +146,8 @@ public:
    **/
    Node const & node(NodeId const id) const;
 
+   Node & node(NodeId const id);
+
    /**
       @brief Adds the edge <tt> {node1_id, node2_id} </tt> to this graph.
 
@@ -224,6 +226,12 @@ Node const & Graph::node(NodeId const id) const
 {
    return _nodes[id];
 }
+
+inline
+Node & Graph::node(NodeId const id)
+{
+   return _nodes[id];
+}
 //END: Inline section