def RandomToleranceGraph(n):
r"""
Returns a random tolerance graph.
The random tolerance graph is built from a random tolerance representation
by using the function `ToleranceGraph`. This representation is a list
`((l_0,r_0,t_0), (l_1,r_1,t_1), ..., (l_k,r_k,t_k))` where `k = n-1` and
`I_i = (l_i,r_i)` denotes a random interval and `t_i` a random positive
value. The width of the representation is limited to n**2 * 2**n.
.. NOTE::
The vertices are named 0, 1, ..., n-1. The tolerance representation used
to create the graph is saved with the graph and can be recovered using
``get_vertex()`` or ``get_vertices()``.
INPUT:
- ``n`` -- number of vertices of the random graph.
EXAMPLE:
Every tolerance graph is perfect. Hence, the chromatic number is equal to
the clique number ::
sage: g = graphs.RandomToleranceGraph(8)
sage: g.clique_number() == g.chromatic_number()
True
TEST::
sage: g = graphs.RandomToleranceGraph(-2)
Traceback (most recent call last):
...
ValueError: The number `n` of vertices must be >= 0.
"""
from sage.misc.prandom import randint
from sage.graphs.generators.intersection import ToleranceGraph
if n < 0:
raise ValueError('The number `n` of vertices must be >= 0.')
W = n**2 * 2**n
tolrep = [
tuple(sorted((randint(0, W), randint(0, W)))) + (randint(0, W), )
for i in range(n)
]
return ToleranceGraph(tolrep)
def RandomBoundedToleranceGraph(n):
r"""
Returns a random bounded tolerance graph.
The random tolerance graph is built from a random bounded
tolerance representation by using the function
`ToleranceGraph`. This representation is a list
`((l_0,r_0,t_0), (l_1,r_1,t_1), ..., (l_k,r_k,t_k))` where
`k = n-1` and `I_i = (l_i,r_i)` denotes a random interval and
`t_i` a random positive value less then or equal to the length
of the interval `I_i`. The width of the representation is
limited to n**2 * 2**n.
.. NOTE::
The tolerance representation used to create the graph can
be recovered using ``get_vertex()`` or ``get_vertices()``.
INPUT:
- ``n`` -- number of vertices of the random graph.
EXAMPLE:
Every (bounded) tolerance graph is perfect. Hence, the
chromatic number is equal to the clique number ::
sage: g = graphs.RandomBoundedToleranceGraph(8)
sage: g.clique_number() == g.chromatic_number()
True
"""
from sage.misc.prandom import randint
from sage.graphs.generators.intersection import ToleranceGraph
W = n**2 * 2**n
tolrep = [
(l_r[0], l_r[1], randint(0, l_r[1] - l_r[0]))
for l_r in [sorted((randint(0, W), randint(0, W))) for i in range(n)]
]
return ToleranceGraph(tolrep)