#13503: Enhancement of `is_triangle_free' addition of `triangles_count' and a
minor
change in `spanning_trees_count'
----------------------------------------------------------+-----------------
Reporter: azi | Owner:
jason, ncohen, rlm
Type: enhancement | Status:
needs_work
Priority: minor | Milestone:
sage-5.4
Component: graph theory | Resolution:
Keywords: triangles, graphs, number of triangles | Work issues:
Report Upstream: N/A | Reviewers:
David Coudert
Authors: Jernej Azarija | Merged in:
Dependencies: | Stopgaps:
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Comment (by dcoudert):
Two interesting (worst case) examples:
{{{
sage: G = graphs.CompleteBipartiteGraph(100,100); M = G.adjacency_matrix()
sage: G.density()
100/199
sage: %timeit not (M*M*M).trace()
5 loops, best of 3: 59.8 ms per loop
sage: %timeit my_is_triangle_free(G)
5 loops, best of 3: 5.66 s per loop
sage:
sage: G = graphs.RandomGNP(200,100/199); M = G.adjacency_matrix()
sage: G.density()
10009/19900
sage: %timeit not (M*M*M).trace()
5 loops, best of 3: 63.8 ms per loop
sage: %timeit my_is_triangle_free(G)
625 loops, best of 3: 300 µs per loop
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13503#comment:14>
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