I want to know the number of 4-colorings for all Johnson solids. This is equivalent to evaluating the flow polynomial for the corresponding polyhedral graphs at $k=4$.
I tried the following to get the data:
Table[{i, 4 GraphData[{"JohnsonSkeleton", i}, "FlowPolynomial"][4]}, {i, 92}]
But for nos. 38-43, 47, 48, 68-82,
Missing["NotAvailable"]
is returned.
I have also tried, for example
FlowPolynomial[GraphData[{"JohnsonSkeleton", 38}], 4]
which causes Mathematica to hang.
Is there another way?
Thanks.
UPDATE
As ilian pointed out in the comments, the command FlowPolynomial
does in fact seem to work-the missing graph numbers just need a lot of memory and time to compute.
I tested the command on a machine with 32GB RAM to confirm ilian's value for $n=38$ (500792391843
)and also got the value for $n=39$ (500453836143
). But $n=40$ exhausted all the RAM and crashed the machine.
So maybe it's unrealistic to ask for the 4-colour numbers for all the Johnson graphs after all. In that case I'd be very happy to settle for approximations of the missing numbers.
EDIT I'm also interested in the same question for the Archimedean solids and their duals (Mathematica is also missing some data for these).
500792391843
after 43 minutes and needed around 21 GB of memory. $\endgroup$GraphData
because it took too long to compute then? $\endgroup$