def DegreeSequenceBipartite(s1, s2):
r"""
Returns a bipartite graph whose two sets have the given
degree sequences.
Given two different sequences of degrees `s_1` and `s_2`,
this functions returns ( if possible ) a bipartite graph
on sets `A` and `B` such that the vertices in `A` have
`s_1` as their degree sequence, while `s_2` is the degree
sequence of the vertices in `B`.
INPUT:
- ``s_1`` -- list of integers corresponding to the degree
sequence of the first set.
- ``s_2`` -- list of integers corresponding to the degree
sequence of the second set.
ALGORITHM:
This function works through the computation of the matrix
given by the Gale-Ryser theorem, which is in this case
the adjacency matrix of the bipartite graph.
EXAMPLES:
If we are given as sequences ``[2,2,2,2,2]`` and ``[5,5]``
we are given as expected the complete bipartite
graph `K_{2,5}` ::
sage: g = graphs.DegreeSequenceBipartite([2,2,2,2,2],[5,5])
sage: g.is_isomorphic(graphs.CompleteBipartiteGraph(5,2))
True
Some sequences being incompatible if, for example, their sums
are different, the functions raises a ``ValueError`` when no
graph corresponding to the degree sequences exists. ::
sage: g = graphs.DegreeSequenceBipartite([2,2,2,2,1],[5,5])
Traceback (most recent call last):
...
ValueError: There exists no bipartite graph corresponding to the given degree sequences
TESTS:
:trac:`12155`::
sage: graphs.DegreeSequenceBipartite([2,2,2,2,2],[5,5]).complement()
Graph on 7 vertices
"""
from sage.combinat.integer_vector import gale_ryser_theorem
from sage.graphs.bipartite_graph import BipartiteGraph
s1 = sorted(s1, reverse=True)
s2 = sorted(s2, reverse=True)
m = gale_ryser_theorem(s1, s2)
if m is False:
raise ValueError(
"There exists no bipartite graph corresponding to the given degree sequences"
)
else:
return Graph(BipartiteGraph(m))
def DegreeSequenceBipartite(s1 ,s2 ):
r"""
Returns a bipartite graph whose two sets have the given
degree sequences.
Given two different sequences of degrees `s_1` and `s_2`,
this functions returns ( if possible ) a bipartite graph
on sets `A` and `B` such that the vertices in `A` have
`s_1` as their degree sequence, while `s_2` is the degree
sequence of the vertices in `B`.
INPUT:
- ``s_1`` -- list of integers corresponding to the degree
sequence of the first set.
- ``s_2`` -- list of integers corresponding to the degree
sequence of the second set.
ALGORITHM:
This function works through the computation of the matrix
given by the Gale-Ryser theorem, which is in this case
the adjacency matrix of the bipartite graph.
EXAMPLES:
If we are given as sequences ``[2,2,2,2,2]`` and ``[5,5]``
we are given as expected the complete bipartite
graph `K_{2,5}` ::
sage: g = graphs.DegreeSequenceBipartite([2,2,2,2,2],[5,5])
sage: g.is_isomorphic(graphs.CompleteBipartiteGraph(5,2))
True
Some sequences being incompatible if, for example, their sums
are different, the functions raises a ``ValueError`` when no
graph corresponding to the degree sequences exists. ::
sage: g = graphs.DegreeSequenceBipartite([2,2,2,2,1],[5,5])
Traceback (most recent call last):
...
ValueError: There exists no bipartite graph corresponding to the given degree sequences
TESTS:
:trac:`12155`::
sage: graphs.DegreeSequenceBipartite([2,2,2,2,2],[5,5]).complement()
Graph on 7 vertices
"""
from sage.combinat.integer_vector import gale_ryser_theorem
from sage.graphs.bipartite_graph import BipartiteGraph
s1 = sorted(s1, reverse = True)
s2 = sorted(s2, reverse = True)
m = gale_ryser_theorem(s1,s2)
if m is False:
raise ValueError("There exists no bipartite graph corresponding to the given degree sequences")
else:
return Graph(BipartiteGraph(m))
