Fix planarity

[Joseph-Edwards]

This PR addresses #669.

For planarity checking, the edge-addition-planarity-suite code needs its graphs to be antisymmetric. Previously, the antisymmetric digraph was constructed in GAP, and then the desired output was constructed in C. This meant that the C code couldn't reason about the user's input digraph, and hence only a minimal rotation system was returned.

Now, the antisymmetric digraph is constructed in C, and the return list in constructed by checking the existence of edges in the user's original input graph.

[Joseph-Edwards]

For some of the SubdigraphHomeomorphicToK[...] functions, I'm not 100% sure what the best output/documentation should be. At the moment, on input D, these functions return subdigraphs G such that, when directions are ignored, it is Homemorphic to K[...]. I don't know if this is desirable (or even the correct use of homeomorphic). For example:

gap> D := CompleteDigraph(4);
<immutable complete digraph with 4 vertices>
gap> SubdigraphHomeomorphicToK4(D);
[ [ 2, 4, 3 ], [ 3, 4, 1 ], [ 4, 2, 1 ], [ 1, 2, 3 ]

An alternative output could be:

[ [ 2, 4, 3 ], [ 3, 4 ], [ 4 ], [ ] ]

It is a question of whether the output should be thought of as a graph (because direction doesn't matter in the case of planarity) or a digraph (because we are in the digraphs package).

I'm happy to change the behaviour to whatever seems the most appropriate, or to provide some more examples.

[Joseph-Edwards]

Provided the tests pass, I think this is good to go @james-d-mitchell

[Joseph-Edwards]

I've just noticed this:

gap> IsPlanarDigraph(HanoiGraph(6));
true
gap> IsPlanarDigraph(DigraphMutableCopy(HanoiGraph(6)));
false

Not sure what's going on, but this probably shouldn't happen. This behaviour exists in the main branch as well. Trying to fix now.

[Joseph-Edwards]

I've just noticed this:

gap> IsPlanarDigraph(HanoiGraph(6));
true
gap> IsPlanarDigraph(DigraphMutableCopy(HanoiGraph(6)));
false

Not sure what's going on, but this probably shouldn't happen. This behaviour exists in the main branch as well. Trying to fix now.

I think this is a problem with HanoiDigraph rather than the planarity stuff (see #698 ).

[james-d-mitchell]

Hmm that seems fishy, the return value shouldn't depend on whether or not the graph is mutable.

[Joseph-Edwards]

@james-d-mitchell HanoiGraph sets the property IsPlanarDigraph to true. My guess is that this value gets returned when dealing with the immutable one, but the planarity actually gets computed (and returns false) in the mutable case.

[james-d-mitchell]

One minor tweak and this is good to go