Talk:Balaban 11-cage

Errors in one picture

Unfortunately there are errors in this picture of the Balaban 11-cage, as noted by Viktor Toth:

When I look at the top of the diagram, I see (going from top to bottom): 8×3 vertices with three neighbors each; next, 8×4 vertices with three neighbors each; and next, 8×8 verticies with TWO neighbors each.

If I ignore the 8×8 two-neighbor vertices, I am left with 56 vertices; another 56 are at the bottom brings the total to 112, which is exactly the number of vertices Balaban’s 11-cage supposedly has.

So from this I have to conclude that the 8×8 two-neighbor vertices at the top (and their counterparts at the bottom), 128 vertices in total, are purely decorative and are not to be seen as actual vertices.

and then:

I looked at the SVG and it could be edited, though it’s a bit of a chore, as editing requires not only removing the unwanted vertices but also lengthening some edges. However, I found other problems with the diagram: the 37th and 45th vertices in the bottom continuous row are orphans, so obviously some edges are misplaced there. So there is a good chance that even after the unwanted vertices are removed, the resulting diagram will still be erroneous. It might be a better idea to re-generate a proper diagram algorithmically.

A correct version can, I hope, be found here. John Baez (talk) 01:40, 3 November 2015 (UTC)