def CompleteMultipartiteGraph(l):
r"""
Returns a complete multipartite graph.
INPUT:
- ``l`` -- a list of integers : the respective sizes
of the components.
EXAMPLE:
A complete tripartite graph with sets of sizes
`5, 6, 8`::
sage: g = graphs.CompleteMultipartiteGraph([5, 6, 8]); g
Multipartite Graph with set sizes [5, 6, 8]: Graph on 19 vertices
It clearly has a chromatic number of 3::
sage: g.chromatic_number()
3
"""
g = Graph()
for i in l:
g = g + CompleteGraph(i)
g = g.complement()
g.name("Multipartite Graph with set sizes "+str(l))
return g
def CompleteMultipartiteGraph(l):
r"""
Returns a complete multipartite graph.
INPUT:
- ``l`` -- a list of integers : the respective sizes
of the components.
EXAMPLE:
A complete tripartite graph with sets of sizes
`5, 6, 8`::
sage: g = graphs.CompleteMultipartiteGraph([5, 6, 8]); g
Multipartite Graph with set sizes [5, 6, 8]: Graph on 19 vertices
It clearly has a chromatic number of 3::
sage: g.chromatic_number()
3
"""
g = Graph()
for i in l:
g = g + CompleteGraph(i)
g = g.complement()
g.name("Multipartite Graph with set sizes " + str(l))
return g
def CompleteMultipartiteGraph(l):
r"""
Returns a complete multipartite graph.
INPUT:
- ``l`` -- a list of integers : the respective sizes
of the components.
EXAMPLES:
A complete tripartite graph with sets of sizes
`5, 6, 8`::
sage: g = graphs.CompleteMultipartiteGraph([5, 6, 8]); g
Multipartite Graph with set sizes [5, 6, 8]: Graph on 19 vertices
It clearly has a chromatic number of 3::
sage: g.chromatic_number()
3
"""
n = sum(l) #getting the number of vertices
r = len(l) #getting the number of partitions
positions = {}
if r > 2: #position code gives bad results on bipartite or isolated graphs
'''
Produce a layout of the vertices so that vertices in the same
vertex set are adjacent and clearly separated from vertices in other
vertex sets.
This is done by calculating the vertices of an r-gon then
calculating the slope between adjacent vertices. We then 'walk'
around the r-gon placing graph vertices in regular intervals between
adjacent vertices of the r-gon.
Makes a nicely organized graph like in this picture:
https://commons.wikimedia.org/wiki/File:Turan_13-4.svg
'''
points = [[cos(2*pi*i/r),sin(2*pi*i/r)] for i in range(r)]
slopes = [[(points[(i+1)%r][0]-points[i%r][0]),
(points[(i+1)%r][1]-points[i%r][1])] for i in range(r)]
counter = 0
for i in range(len(l)):
vertex_set_size = l[i]+1
for j in range(1,vertex_set_size):
x = points[i][0]+slopes[i][0]*j/(vertex_set_size)
y = points[i][1]+slopes[i][1]*j/(vertex_set_size)
positions[counter] = (x,y)
counter += 1
g = Graph()
for i in l:
g = g + CompleteGraph(i)
g = g.complement()
g.set_pos(positions)
g.name("Multipartite Graph with set sizes "+str(l))
return g
def CompleteMultipartiteGraph(l):
r"""
Return a complete multipartite graph.
INPUT:
- ``l`` -- a list of integers; the respective sizes of the components
PLOTTING: Produce a layout of the vertices so that vertices in the same
vertex set are adjacent and clearly separated from vertices in other vertex
sets.
This is done by calculating the vertices of an `r`-gon then calculating the
slope between adjacent vertices. We then 'walk' around the `r`-gon placing
graph vertices in regular intervals between adjacent vertices of the
`r`-gon.
Makes a nicely organized graph like in this picture:
https://commons.wikimedia.org/wiki/File:Turan_13-4.svg
EXAMPLES:
A complete tripartite graph with sets of sizes `5, 6, 8`::
sage: g = graphs.CompleteMultipartiteGraph([5, 6, 8]); g
Multipartite Graph with set sizes [5, 6, 8]: Graph on 19 vertices
It clearly has a chromatic number of 3::
sage: g.chromatic_number()
3
"""
r = len(l) # getting the number of partitions
name = "Multipartite Graph with set sizes {}".format(l)
if not r:
g = Graph()
elif r == 1:
g = Graph(l[0])
g._line_embedding(range(l[0]), first=(0, 0), last=(l[0], 0))
elif r == 2:
g = CompleteBipartiteGraph(l[0], l[1])
g.name(name)
else:
# This position code gives bad results on bipartite or isolated graphs
points = [(cos(2 * pi * i / r), sin(2 * pi * i / r)) for i in range(r)]
slopes = [(points[(i + 1) % r][0] - points[i % r][0],
points[(i + 1) % r][1] - points[i % r][1]) for i in range(r)]
counter = 0
positions = {}
for i in range(r):
vertex_set_size = l[i] + 1
for j in range(1, vertex_set_size):
x = points[i][0] + slopes[i][0] * j / vertex_set_size
y = points[i][1] + slopes[i][1] * j / vertex_set_size
positions[counter] = (x, y)
counter += 1
g = Graph(sum(l))
s = 0
for i in l:
g.add_clique(range(s, s + i))
s += i
g = g.complement()
g.set_pos(positions)
g.name(name)
return g
def CompleteMultipartiteGraph(l):
r"""
Returns a complete multipartite graph.
INPUT:
- ``l`` -- a list of integers : the respective sizes
of the components.
EXAMPLE:
A complete tripartite graph with sets of sizes
`5, 6, 8`::
sage: g = graphs.CompleteMultipartiteGraph([5, 6, 8]); g
Multipartite Graph with set sizes [5, 6, 8]: Graph on 19 vertices
It clearly has a chromatic number of 3::
sage: g.chromatic_number()
3
"""
n = sum(l) #getting the number of vertices
r = len(l) #getting the number of partitions
positions = {}
if r > 2: #position code gives bad results on bipartite or isolated graphs
'''
Produce a layout of the vertices so that vertices in the same
vertex set are adjecent and clearly separated from vertices in other
vertex sets.
This is done by calculating the vertices of an r-gon then
calculating the slope between adjacent vertices. We then 'walk'
around the r-gon placing graph vertices in regular intervals between
adjacent vertices of the r-gon.
Makes a nicely organized graph like in this picture:
https://commons.wikimedia.org/wiki/File:Turan_13-4.svg
'''
points = [[cos(2*pi*i/r),sin(2*pi*i/r)] for i in range(r)]
slopes = [[(points[(i+1)%r][0]-points[i%r][0]),
(points[(i+1)%r][1]-points[i%r][1])] for i in range(r)]
counter = 0
for i in range(len(l)):
vertex_set_size = l[i]+1
for j in range(1,vertex_set_size):
x = points[i][0]+slopes[i][0]*j/(vertex_set_size)
y = points[i][1]+slopes[i][1]*j/(vertex_set_size)
positions[counter] = (x,y)
counter += 1
g = Graph()
for i in l:
g = g + CompleteGraph(i)
g = g.complement()
g.set_pos(positions)
g.name("Multipartite Graph with set sizes "+str(l))
return g
