Improve ChromaticNumber

[james-d-mitchell]

Currently, ChromaticNumber does a linear search for the chromatic number. It'd be much better if it did a binary search.

[wilfwilson]

It is not clear whether this is actually faster. Binary search (happens) typically by repeatedly under- and over-estimating the solution. For chromatic number, it is normally much quicker to determine whether your guess is an overestimate (simply find a colouring with that many colours) than an underestimate (this requires proving that no colouring is proper, which is perhaps very expensive). So perhaps the current method, which I assume starts with an overestimate and decreases that estimate linearly, is the fastest way in general. We could do experiments to determine this.

[james-d-mitchell]

Fair point @wilfwilson, maybe the issues is that we should just improve the ChromaticNumber method so it's faster, perhaps using Leonard Soicher's approach.

[wilfwilson]

And Leonard feels that, for his approach, the binary search would be appropriate.