def graph_coloring(G: List[Node]) -> int:
color = [0] * len(G)
ordered = lexBFS(G)
for v in ordered:
neigs = G[v].out
used = {color[u] for u in neigs}
min_free_col = 1
while min_free_col <= len(G):
if min_free_col not in used:
break
min_free_col += 1
color[v] = min_free_col
return max(color)
def get_RN(G: List[Node]) -> List[set[int]]:
RN = [set() for _ in range(len(G))]
parent = [0] * len(G)
ord = lexBFS(G)
for v in ord:
# RN[v] - zbiór sąsiadów pojawiających się wcześniej niż v
for el in ord:
if el == v:
break
if el in G[v].out:
RN[v].add(el)
parent[v] = el
return RN
def biggest_clique(G: List[Node]) -> int:
""" returns size of the biggest clique in given chordal graph """
assert (is_chordal(G)), "Received graph is not chordal! "
ord = lexBFS(G)
max_size = 0
RN = [set() for _ in range(len(G))
] # RN[v] - zbiór sąsiadów pojawiających się wcześniej niż v
for v in ord:
for el in ord:
if el == v:
break
if el in G[v].out:
RN[v].add(el)
max_size = max(max_size, len(RN[v]) + 1)
return max_size
def clique_tree(G: List[Node]):
ord = lexBFS(G)
parent = [0] * len(G)
cliques = [] # list of all cliques
clique_par = [0] * len(G) # index of parent clique
clique_nr = [0] * len(G) # nr of clique corresponding to vertex i
# creating RN list
RN = [set() for _ in range(len(G))
] # RN[v] - zbiór sąsiadów pojawiających się wcześniej niż v
for v in ord:
for el in ord:
if el == v:
break
if el in G[v].out:
RN[v].add(el)
parent[v] = el
# creating tree
v = ord[0]
cliques.append({v})
clique_nr[v] = 0
clique_par[0] = 0
for i in range(1, len(ord)):
v = ord[i]
# print(" \t at v ", v)
if len(RN[v].symmetric_difference(cliques[clique_nr[parent[v]]])) == 0:
clique_nr[v] = clique_nr[parent[v]]
cliques[clique_nr[v]].add(v)
# print(" adding to cliq nr ", clique_nr[v], " and now " ,cliques[clique_nr[v]])
# print(" now clique is : ", cliques[clique_nr[v])
else:
cliques.append(RN[v] | {v})
newInd = len(cliques) - 1
clique_nr[v] = newInd
# print(" new clique nr ", newInd, " w parent ", clique_nr[parent[v]])
# print(" now clique is : ", cliques[clique_nr[v])
clique_par[newInd] = clique_nr[parent[v]]
print(cliques)
print(clique_par)
graphs = []
for name in os.listdir("res/chordal"):
graphs.append(f"res/chordal/{name}")
def test_lex_BFS(G: List[Node], vs: List[int]) -> bool:
n = len(G)
pi = [None] * n
for i, v in enumerate(vs):
pi[v] = i
for i in range(n - 1):
for j in range(i + 1, n - 1):
Ni = G[vs[i]].out
Nj = G[vs[j]].out
verts = [pi[v] for v in Nj - Ni if pi[v] < i]
if verts:
viable = [pi[v] for v in Ni - Nj]
if not viable or min(verts) <= min(viable):
return False
return True
for graph in graphs:
G = create_graph(graph)
vs = lexBFS(G)
graph = graph.split("/")[-1]
print(test_lex_BFS(G, vs))
def is_chordal(G: List[Node]) -> bool:
ordered_v = lexBFS(G)
return is_PEO(G, ordered_v)