Hi,
how can I generate, in a fast enough way, connected graphs for which the
clique complex is pure, ie, for which all containmentwise maximal cliques
are of the same size ?
Fast enough here means that I can produce examples of such graphs with 20
vertices, edge degrees between 10 and 14 (an example of such a graph on
diagonals in a regular 7-gon with edges being pairwise noncrossing
diagonals and the resulting clique complex the dual associahedron of
dimension 4).
What I got so far is:
from sage.graphs.independent_sets import IndependentSets
for G in graphs.nauty_geng("20 -c -d10 -D14"):
cliques = IndependentSets(G, maximal = True, complement = True)
sizes = map(len,cliques)
size_min = min(sizes)
if size_min > 4:
size_max = max(sizes)
if size_min == size_max:
print list(cliques)
But this seems to be too slow, already because it takes too long for this
to turn the graph6 string from nauty into a sage graph.
Does someone know how I can do this computation more low-level? Best would
clearly be to teach nauty to only iter through such graphs, but that does
not seem to be possible...
Thanks, Christian
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