def _is_valid_ribbon(self, ribbon):
r"""
Return ``True`` if a ribbon has at most one anchor, no vertex has two
or more anchors, and every hanging poset is d-complete.
INPUT:
- ``ribbon`` -- a list of elements that form a ribbon in your poset
TESTS::
sage: P = posets.RibbonPoset(5, [2])
sage: P._is_valid_ribbon([0,1,2,3,4])
True
sage: P._is_valid_ribbon([2])
False
sage: P._is_valid_ribbon([2,3,4])
True
sage: P._is_valid_ribbon([2,3])
True
"""
ribbon = [self._element_to_vertex(x) for x in ribbon]
G = self._hasse_diagram
G_un = G.to_undirected().copy(immutable=False)
R = G.subgraph(ribbon)
num_anchors = 0
for r in ribbon:
anchor_neighbors = set(G.neighbors_out(r)).difference(
set(R.neighbors_out(r)))
if len(anchor_neighbors) == 1:
num_anchors += 1
elif len(anchor_neighbors) > 1:
return False
for lc in G.neighbors_in(r):
if lc in ribbon:
continue
G_un.delete_edge(lc, r)
P = Poset(
G.subgraph(G_un.connected_component_containing_vertex(lc)))
if P.top() != lc or not P.is_d_complete():
return False
G_un.add_edge(lc, r)
return True
