# treewidth()

Is there a bug with the treewidth function? I let G be a tree on 5 nodes and calculate a tree decomposition. However, the answer I get does not seem to be correct as the set of vertices returned are {0},{1},{2,3},{3},{3,4}. The definition of a tree decomposition requires that if (i,j) is an edge in G then there is a bag that contains both i and j. But clearly the above tree decomposition does not have satisfy this property?

To illustrate with a concrete example (not the one above):

M = Matrix([[0, 0, 1, 0, 1],
[0, 0, 1, 0, 0],
[1, 1, 0, 1, 0],
[0, 0, 1, 0, 0],
[1, 0, 0, 0, 0]])
g = Graph(M)
T = g.treewidth(certificate=True)
T.vertices()


This returns:

[{0}, {2}, {2, 3}, {0, 4}, {1, 2}]


Clearly (0,2) is an edge of the original graph but the answer above does not have a bag that contains both 0 and 2.

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( 2015-03-03 05:49:10 -0500 )edit

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Here it is ! This is now ticket #17893. There was a problem indeed, but not in the actual computations. I was trying to simplify the final tree too much, and well. To the point that some things that had their importance actually vanished :-P

It is updated. Very very slightly more time-consuming, but a clearer code. Good deal.

By the way it is in 'needs_review', i.e. somebody (anybody) needs to double check it before it makes it into Sage.

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