43 lines
1.1 KiB
Python
43 lines
1.1 KiB
Python
|
"""
|
||
|
|
Ramsey numbers.
|
||
|
|
"""
|
||
|
|
import networkx as nx
|
||
|
|
from ...utils import arbitrary_element
|
||
|
|
|
||
|
|
__all__ = ["ramsey_R2"]
|
||
|
|
|
||
|
|
|
||
|
|
def ramsey_R2(G):
|
||
|
|
r"""Compute the largest clique and largest independent set in `G`.
|
||
|
|
|
||
|
|
This can be used to estimate bounds for the 2-color
|
||
|
|
Ramsey number `R(2;s,t)` for `G`.
|
||
|
|
|
||
|
|
This is a recursive implementation which could run into trouble
|
||
|
|
for large recursions. Note that self-loop edges are ignored.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
G : NetworkX graph
|
||
|
|
Undirected graph
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
max_pair : (set, set) tuple
|
||
|
|
Maximum clique, Maximum independent set.
|
||
|
|
"""
|
||
|
|
if not G:
|
||
|
|
return set(), set()
|
||
|
|
|
||
|
|
node = arbitrary_element(G)
|
||
|
|
nbrs = (nbr for nbr in nx.all_neighbors(G, node) if nbr != node)
|
||
|
|
nnbrs = nx.non_neighbors(G, node)
|
||
|
|
c_1, i_1 = ramsey_R2(G.subgraph(nbrs).copy())
|
||
|
|
c_2, i_2 = ramsey_R2(G.subgraph(nnbrs).copy())
|
||
|
|
|
||
|
|
c_1.add(node)
|
||
|
|
i_2.add(node)
|
||
|
|
# Choose the larger of the two cliques and the larger of the two
|
||
|
|
# independent sets, according to cardinality.
|
||
|
|
return max(c_1, c_2, key=len), max(i_1, i_2, key=len)
|