NOTE: Problems with PlanarGraphQ

From GraphData

In[]:=
GraphData["Planar"]
Out[]=
In[]:=
GraphData/@Take[%,6]
Out[]=

From “House of Graphs”

In[]:=
Import["https://hog.grinvin.org/data/planar/planar_graphs/planar_conn.5.g6"]
Out[]=
In[]:=
GetPlanarGraphs[n_Integer]:=Import[StringTemplate["https://hog.grinvin.org/data/planar/planar_graphs/planar_conn.``.g6"][n]]
In[]:=
GetPlanarGraphs[2]
Out[]=
In[]:=
GetPlanarGraphs[3]
Out[]=

,

In[]:=
GetPlanarGraphs[4]
Out[]=
In[]:=
EdgeList

Out[]=
{12,13,14,23,24,34}
In[]:=
AllReversals[g_Graph]:=With[{e=List@@@EdgeList[g]},MapThread[Construct,{#,e}]&/@Tuples[{Identity,Reverse},Length[e]]]
In[]:=
AllReversals

Out[]=
(Should also check termination; check there was an update)
In[]:=
WolframModel[{{x,y}}{{x,z},{y,z},{z,z}},#,1,"FinalState"]&/@%23
Out[]=

Testing Code

Working around a PlanarGraphQ crash bug:

2,2  3,2 rules

1,2  3,2

1,2  2,2