> Consider: g = graph({1:[2,3,4,5],2:[3,5],4:[3,5]}). Hahahahhahaaha ! Dead right :-)
And the code works anyway because the tree it returns actually is *NOT* a BFS tree :-) sage: g.lex_BFS(tree = True)[1].edges() [(2, 1, None), (3, 2, None), (4, 5, None), (5, 2, None)] Two (obvious) black patches in my previous proof : * It totally ignores the edges between classes of vertices with the same distance to the source -- precisely what your counter-example destroys. * without considering "the last neighbor of v discovered before v itself", its process does not ensure that the neighborhood of a removed vertex is indeed simplicial. Very bad indeed :-) For a time I thought I would be able to patch my proof, but in the end I don't get how this recognition algorithm works... Which is a pity because I am sure I had found a clear explanation in a paper when I implemented all that stuff. What I need right now is some sleep though. Sounds like this will really require a patch :-) Thank you for your perseverance ! At the least I enjoyed the time thinking of this algorithm again and (re ?)-learned a few nice tricks ;-) Good niiiiiiiiight ! Nathann -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org