#6074: Planar graph generation
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Reporter: rlm | Owner: rlm
Type: enhancement | Status: new
Priority: major | Milestone: sage-wishlist
Component: graph theory | Keywords:
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Essentially, this shouldn't be too difficult to implement in Sage:
http://cs.anu.edu.au/~bdm/papers/plantri-full.pdf
The basic steps to generate plane graphs (graphs embedded in the plane) of
minimum degree at least `d`, connectivity at least `k`, number of edges at
least `e`, and max face size at most `p`, are:
1. Implement section 1.3 of the above paper. This allows for a much faster
implementation of automorphism group and isomorphism in the case of plane
graphs.
2. Generate all planar triangluations, with min degree at least
`max(d,3)`, connectivity at least `max(k,3)`. This is described in section
1.2, mainly the third paragraph. Essentially, you start with K_4, and you
augment by one of the three moves E_3, E_4, or E_5. The "backwards" step
in canonical augmentation here is to first try to remove the least-labeled
vertex of degree 3, i.e. try to undo E_3 if possible, or degree 4 if that
is possible, i.e. try to undo E_4 if possible, then finally checking for
degree 5.
3. Use these, together with edge deletion and canonical augmentation, to
generate all plane graphs.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6074>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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