diff --git a/networkx/algorithms/bipartite/matching.py b/networkx/algorithms/bipartite/matching.py
index 279e01604..2059d6bdf 100644
--- a/networkx/algorithms/bipartite/matching.py
+++ b/networkx/algorithms/bipartite/matching.py
@@ -346,14 +346,14 @@ def _is_connected_by_alternating_path(G, v, matched_edges, unmatched_edges, targ
         will continue only through edges *not* in the given matching.
 
         """
-        if along_matched:
-            edges = itertools.cycle([matched_edges, unmatched_edges])
-        else:
-            edges = itertools.cycle([unmatched_edges, matched_edges])
         visited = set()
-        stack = [(u, iter(G[u]), next(edges))]
+        # Follow matched edges when depth is even,
+        # and follow unmatched edges when depth is odd.
+        initial_depth = 0 if along_matched else 1
+        stack = [(u, iter(G[u]), initial_depth)]
         while stack:
-            parent, children, valid_edges = stack[-1]
+            parent, children, depth = stack[-1]
+            valid_edges = matched_edges if depth % 2 else unmatched_edges
             try:
                 child = next(children)
                 if child not in visited:
@@ -361,7 +361,7 @@ def _is_connected_by_alternating_path(G, v, matched_edges, unmatched_edges, targ
                         if child in targets:
                             return True
                         visited.add(child)
-                        stack.append((child, iter(G[child]), next(edges)))
+                        stack.append((child, iter(G[child]), depth + 1))
             except StopIteration:
                 stack.pop()
         return False
diff --git a/networkx/algorithms/tournament.py b/networkx/algorithms/tournament.py
index 2205f5556..cedd2bc06 100644
--- a/networkx/algorithms/tournament.py
+++ b/networkx/algorithms/tournament.py
@@ -276,7 +276,6 @@ def is_reachable(G, s, t):
            tournaments."
            *Electronic Colloquium on Computational Complexity*. 2001.
            <http://eccc.hpi-web.de/report/2001/092/>
-
     """
 
     def two_neighborhood(G, v):

diff --git a/networkx/algorithms/bipartite/tests/test_matching.py b/networkx/algorithms/bipartite/tests/test_matching.py
index d4fcd9802..3c6cc35fd 100644
--- a/networkx/algorithms/bipartite/tests/test_matching.py
+++ b/networkx/algorithms/bipartite/tests/test_matching.py
@@ -180,6 +180,16 @@ class TestMatching:
         for u, v in G.edges():
             assert u in vertex_cover or v in vertex_cover
 
+    def test_vertex_cover_issue_3306(self):
+        G = nx.Graph()
+        edges = [(0, 2), (1, 0), (1, 1), (1, 2), (2, 2)]
+        G.add_edges_from([((i, "L"), (j, "R")) for i, j in edges])
+
+        matching = maximum_matching(G)
+        vertex_cover = to_vertex_cover(G, matching)
+        for u, v in G.edges():
+            assert u in vertex_cover or v in vertex_cover
+
     def test_unorderable_nodes(self):
         a = object()
         b = object()
diff --git a/networkx/algorithms/tests/test_tournament.py b/networkx/algorithms/tests/test_tournament.py
index 8de6f7c3e..42a31f9be 100644
--- a/networkx/algorithms/tests/test_tournament.py
+++ b/networkx/algorithms/tests/test_tournament.py
@@ -1,132 +1,157 @@
 """Unit tests for the :mod:`networkx.algorithms.tournament` module."""
 from itertools import combinations
-
-
+import pytest
 from networkx import DiGraph
 from networkx.algorithms.tournament import is_reachable
 from networkx.algorithms.tournament import is_strongly_connected
 from networkx.algorithms.tournament import is_tournament
 from networkx.algorithms.tournament import random_tournament
 from networkx.algorithms.tournament import hamiltonian_path
+from networkx.algorithms.tournament import score_sequence
+from networkx.algorithms.tournament import tournament_matrix
+from networkx.algorithms.tournament import index_satisfying
+
+
+def test_condition_not_satisfied():
+    condition = lambda x: x > 0
+    iter_in = [0]
+    assert index_satisfying(iter_in, condition) == 1
+
+
+def test_empty_iterable():
+    condition = lambda x: x > 0
+    with pytest.raises(ValueError):
+        index_satisfying([], condition)
 
 
-class TestIsTournament:
-    """Unit tests for the :func:`networkx.tournament.is_tournament`
-    function.
+def test_is_tournament():
+    G = DiGraph()
+    G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
+    assert is_tournament(G)
+
+
+def test_self_loops():
+    """A tournament must have no self-loops."""
+    G = DiGraph()
+    G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
+    G.add_edge(0, 0)
+    assert not is_tournament(G)
+
+
+def test_missing_edges():
+    """A tournament must not have any pair of nodes without at least
+    one edge joining the pair.
 
     """
+    G = DiGraph()
+    G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3)])
+    assert not is_tournament(G)
+
 
-    def test_is_tournament(self):
-        G = DiGraph()
-        G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
+def test_bidirectional_edges():
+    """A tournament must not have any pair of nodes with greater
+    than one edge joining the pair.
+
+    """
+    G = DiGraph()
+    G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
+    G.add_edge(1, 0)
+    assert not is_tournament(G)
+
+
+def test_graph_is_tournament():
+    for _ in range(10):
+        G = random_tournament(5)
         assert is_tournament(G)
 
-    def test_self_loops(self):
-        """A tournament must have no self-loops."""
-        G = DiGraph()
-        G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
-        G.add_edge(0, 0)
-        assert not is_tournament(G)
 
-    def test_missing_edges(self):
-        """A tournament must not have any pair of nodes without at least
-        one edge joining the pair.
+def test_graph_is_tournament_seed():
+    for _ in range(10):
+        G = random_tournament(5, seed=1)
+        assert is_tournament(G)
 
-        """
-        G = DiGraph()
-        G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3)])
-        assert not is_tournament(G)
 
-    def test_bidirectional_edges(self):
-        """A tournament must not have any pair of nodes with greater
-        than one edge joining the pair.
+def test_graph_is_tournament_one_node():
+    G = random_tournament(1)
+    assert is_tournament(G)
 
-        """
-        G = DiGraph()
-        G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
-        G.add_edge(1, 0)
-        assert not is_tournament(G)
 
+def test_graph_is_tournament_zero_node():
+    G = random_tournament(0)
+    assert is_tournament(G)
 
-class TestRandomTournament:
-    """Unit tests for the :func:`networkx.tournament.random_tournament`
-    function.
 
-    """
+def test_hamiltonian_empty_graph():
+    path = hamiltonian_path(DiGraph())
+    assert len(path) == 0
 
-    def test_graph_is_tournament(self):
-        for n in range(10):
-            G = random_tournament(5)
-            assert is_tournament(G)
 
-    def test_graph_is_tournament_seed(self):
-        for n in range(10):
-            G = random_tournament(5, seed=1)
-            assert is_tournament(G)
+def test_path_is_hamiltonian():
+    G = DiGraph()
+    G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
+    path = hamiltonian_path(G)
+    assert len(path) == 4
+    assert all(v in G[u] for u, v in zip(path, path[1:]))
 
 
-class TestHamiltonianPath:
-    """Unit tests for the :func:`networkx.tournament.hamiltonian_path`
-    function.
+def test_hamiltonian_cycle():
+    """Tests that :func:`networkx.tournament.hamiltonian_path`
+    returns a Hamiltonian cycle when provided a strongly connected
+    tournament.
 
     """
+    G = DiGraph()
+    G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
+    path = hamiltonian_path(G)
+    assert len(path) == 4
+    assert all(v in G[u] for u, v in zip(path, path[1:]))
+    assert path[0] in G[path[-1]]
 
-    def test_path_is_hamiltonian(self):
-        G = DiGraph()
-        G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
-        path = hamiltonian_path(G)
-        assert len(path) == 4
-        assert all(v in G[u] for u, v in zip(path, path[1:]))
 
-    def test_hamiltonian_cycle(self):
-        """Tests that :func:`networkx.tournament.hamiltonian_path`
-        returns a Hamiltonian cycle when provided a strongly connected
-        tournament.
+def test_score_sequence_edge():
+    G = DiGraph([(0, 1)])
+    assert score_sequence(G) == [0, 1]
 
-        """
-        G = DiGraph()
-        G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
-        path = hamiltonian_path(G)
-        assert len(path) == 4
-        assert all(v in G[u] for u, v in zip(path, path[1:]))
-        assert path[0] in G[path[-1]]
 
+def test_score_sequence_triangle():
+    G = DiGraph([(0, 1), (1, 2), (2, 0)])
+    assert score_sequence(G) == [1, 1, 1]
 
-class TestReachability:
-    """Unit tests for the :func:`networkx.tournament.is_reachable`
-    function.
 
-    """
+def test_tournament_matrix():
+    np = pytest.importorskip("numpy")
+    npt = pytest.importorskip("numpy.testing")
+    G = DiGraph([(0, 1)])
+    m = tournament_matrix(G)
+    npt.assert_array_equal(m.todense(), np.array([[0, 1], [-1, 0]]))
 
-    def test_reachable_pair(self):
-        """Tests for a reachable pair of nodes."""
-        G = DiGraph([(0, 1), (1, 2), (2, 0)])
-        assert is_reachable(G, 0, 2)
 
-    def test_same_node_is_reachable(self):
-        """Tests that a node is always reachable from itself."""
-        # G is an arbitrary tournament on ten nodes.
-        G = DiGraph(sorted(p) for p in combinations(range(10), 2))
-        assert all(is_reachable(G, v, v) for v in G)
+def test_reachable_pair():
+    """Tests for a reachable pair of nodes."""
+    G = DiGraph([(0, 1), (1, 2), (2, 0)])
+    assert is_reachable(G, 0, 2)
 
-    def test_unreachable_pair(self):
-        """Tests for an unreachable pair of nodes."""
-        G = DiGraph([(0, 1), (0, 2), (1, 2)])
-        assert not is_reachable(G, 1, 0)
 
+def test_same_node_is_reachable():
+    """Tests that a node is always reachable from it."""
+    # G is an arbitrary tournament on ten nodes.
+    G = DiGraph(sorted(p) for p in combinations(range(10), 2))
+    assert all(is_reachable(G, v, v) for v in G)
 
-class TestStronglyConnected:
-    """Unit tests for the
-    :func:`networkx.tournament.is_strongly_connected` function.
 
-    """
+def test_unreachable_pair():
+    """Tests for an unreachable pair of nodes."""
+    G = DiGraph([(0, 1), (0, 2), (1, 2)])
+    assert not is_reachable(G, 1, 0)
+
+
+def test_is_strongly_connected():
+    """Tests for a strongly connected tournament."""
+    G = DiGraph([(0, 1), (1, 2), (2, 0)])
+    assert is_strongly_connected(G)
 
-    def test_is_strongly_connected(self):
-        """Tests for a strongly connected tournament."""
-        G = DiGraph([(0, 1), (1, 2), (2, 0)])
-        assert is_strongly_connected(G)
 
-    def test_not_strongly_connected(self):
-        """Tests for a tournament that is not strongly connected."""
-        G = DiGraph([(0, 1), (0, 2), (1, 2)])
-        assert not is_strongly_connected(G)
+def test_not_strongly_connected():
+    """Tests for a tournament that is not strongly connected."""
+    G = DiGraph([(0, 1), (0, 2), (1, 2)])
+    assert not is_strongly_connected(G)

hopcroft_karp_matching / to_vertex_cover bug
`to_vertex_cover` must give the **minimum vertex cover** as documented. Wasn't it fixed in #2384 ?
The following code gives random results:

```python
import networkx as nx

nodesU = ['r1','r2','r3','r4','r5','r6','r7','r8']
nodesV = ['c1','c2','c3','c4','c5','c6','c7','c8']
edges = [
        ('r1','c2'),('r1','c4'),('r1','c5'),('r1','c8'),
        ('r2','c1'),('r2','c2'),('r2','c3'),('r2','c6'),('r2','c7'),
        ('r3','c4'),('r3','c5'),
        ('r4','c2'),('r4','c8'),
        ('r5','c2'),('r5','c8'),
        ('r6','c1'),('r6','c2'),('r6','c3'),('r6','c5'),('r6','c6'),('r6','c7'),
        ('r7','c2'),('r7','c8'),
        ('r8','c2'),('r8','c4')]

G = nx.Graph()
G.add_nodes_from(nodesU, bipartite=0)
G.add_nodes_from(nodesV, bipartite=1)
G.add_edges_from(edges)
M = nx.bipartite.hopcroft_karp_matching(G, top_nodes = nodesU)
print('matchings M = ', M)
print('|M|  = ', len(M))

K = nx.bipartite.to_vertex_cover(G, M, top_nodes = nodesU)
print('minimum cover K = ', K)
print('|K|  = ', len(K))
```

Here are the results of multiple runs:
```
matchings M =  {'c1': 'r6', 'r7': 'c2', 'r5': 'c8', 'r1': 'c5', 'r8': 'c4', 'r6': 'c1', 'c5': 'r1', 'c8': 'r5', 'r2': 'c7', 'c7': 'r2', 'c2': 'r7', 'c4': 'r8'}
|M|  =  12
minimum cover K =  {'c1', 'c5', 'c7', 'c2', 'c8', 'c4'}
|K|  =  6

matchings M =  {'c6': 'r6', 'r6': 'c6', 'r1': 'c4', 'r4': 'c2', 'c3': 'r2', 'r5': 'c8', 'c5': 'r3', 'r3': 'c5', 'c8': 'r5', 'r2': 'c3', 'c4': 'r1', 'c2': 'r4'}
|M|  =  12
minimum cover K =  {'c6', 'r6', 'c4', 'c5', 'c2', 'c3', 'c8', 'r2'}
|K|  =  8

matchings M =  {'c8': 'r7', 'r7': 'c8', 'c1': 'r2', 'r3': 'c4', 'r6': 'c7', 'c5': 'r1', 'c2': 'r4', 'c7': 'r6', 'r4': 'c2', 'r2': 'c1', 'c4': 'r3', 'r1': 'c5'}
|M|  =  12
minimum cover K =  {'r2', 'c8', 'c4', 'c2', 'c5'}
|K|  =  5

matchings M =  {'r3': 'c4', 'r6': 'c1', 'r1': 'c5', 'c2': 'r7', 'r7': 'c2', 'c8': 'r5', 'r2': 'c7', 'c5': 'r1', 'r5': 'c8', 'c1': 'r6', 'c7': 'r2', 'c4': 'r3'}
|M|  =  12
minimum cover K =  {'c8', 'c5', 'c7', 'r6', 'c2', 'c4'}
|K|  =  6
```

I'm using networkx 2.2 on debian/python3 and windows miniconda3.
The graph is from: [http://tryalgo.org/en/matching/2016/08/05/konig/](http://tryalgo.org/en/matching/2016/08/05/konig/)

Also why `hopcroft_karp_matching` returns matchings and opposite edges ?
networkx/algorithms/bipartite/tests/test_matching.py::TestMatching::test_vertex_cover_issue_3306
networkx/algorithms/bipartite/tests/test_matching.py::TestMatching::test_issue_2127 networkx/algorithms/bipartite/tests/test_matching.py::TestMatching::test_vertex_cover_issue_2384 networkx/algorithms/bipartite/tests/test_matching.py::TestMatching::test_unorderable_nodes networkx/algorithms/bipartite/tests/test_matching.py::test_eppstein_matching networkx/algorithms/bipartite/tests/test_matching.py::TestMinimumWeightFullMatching::test_minimum_weight_full_matching_incomplete_graph networkx/algorithms/bipartite/tests/test_matching.py::TestMinimumWeightFullMatching::test_minimum_weight_full_matching_with_no_full_matching networkx/algorithms/bipartite/tests/test_matching.py::TestMinimumWeightFullMatching::test_minimum_weight_full_matching_square networkx/algorithms/bipartite/tests/test_matching.py::TestMinimumWeightFullMatching::test_minimum_weight_full_matching_smaller_left networkx/algorithms/bipartite/tests/test_matching.py::TestMinimumWeightFullMatching::test_minimum_weight_full_matching_smaller_top_nodes_right networkx/algorithms/bipartite/tests/test_matching.py::TestMinimumWeightFullMatching::test_minimum_weight_full_matching_smaller_right networkx/algorithms/bipartite/tests/test_matching.py::TestMinimumWeightFullMatching::test_minimum_weight_full_matching_negative_weights networkx/algorithms/bipartite/tests/test_matching.py::TestMinimumWeightFullMatching::test_minimum_weight_full_matching_different_weight_key networkx/algorithms/tests/test_tournament.py::test_condition_not_satisfied networkx/algorithms/tests/test_tournament.py::test_empty_iterable networkx/algorithms/tests/test_tournament.py::test_is_tournament networkx/algorithms/tests/test_tournament.py::test_self_loops networkx/algorithms/tests/test_tournament.py::test_missing_edges networkx/algorithms/tests/test_tournament.py::test_bidirectional_edges networkx/algorithms/tests/test_tournament.py::test_graph_is_tournament networkx/algorithms/tests/test_tournament.py::test_graph_is_tournament_seed networkx/algorithms/tests/test_tournament.py::test_graph_is_tournament_one_node networkx/algorithms/tests/test_tournament.py::test_graph_is_tournament_zero_node networkx/algorithms/tests/test_tournament.py::test_hamiltonian_empty_graph networkx/algorithms/tests/test_tournament.py::test_path_is_hamiltonian networkx/algorithms/tests/test_tournament.py::test_hamiltonian_cycle networkx/algorithms/tests/test_tournament.py::test_score_sequence_edge networkx/algorithms/tests/test_tournament.py::test_score_sequence_triangle networkx/algorithms/tests/test_tournament.py::test_tournament_matrix networkx/algorithms/tests/test_tournament.py::test_reachable_pair networkx/algorithms/tests/test_tournament.py::test_same_node_is_reachable networkx/algorithms/tests/test_tournament.py::test_unreachable_pair networkx/algorithms/tests/test_tournament.py::test_is_strongly_connected networkx/algorithms/tests/test_tournament.py::test_not_strongly_connected