Testing Bounds for Equality

Patrick’s INP code is available on GitHub at:

https://github.com/IndependenceNumberProject/inp

One cool thing you can do is test any of the coded invariants for how often it predicts the value of alpha for graphs of order up to a user-specified n. Residue and Lovasz’s theta are, in practice, the current best lower and upper bounds. Here’s what INP tells us (for graphs up to order 8):

sage: INPGraph.survey(INPGraph.residue, 8)
Counting graphs of order 8… 2079
Testing…
411 out of 2079 graphs of order 8 were predicted by residue.

sage: INPGraph.survey(INPGraph.lovasz_theta, 8)
Counting graphs of order 8… 2079
Testing…
1958 out of 2079 graphs of order 8 were predicted by lovasz_theta.

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