On Jun 15, 2023, at 18:20, S Joshua Swamidass <[email protected]> wrote:
> It's well known that the graph-isomorphism problem is NP

While P is contained in NP, I don't think that's the NP you mean.

I suspect you may be thinking of subgraph isomorphism, which is NP-hard. Graph 
isomorphism may be quasi-polynomial time, if Babai's (unpublished) claim is 
correct.

Also, "Isomorphism of graphs of bounded valence can be tested in polynomial 
time" - https://www.sciencedirect.com/science/article/pii/0022000082900095 .


> So here is my question. What are the cases that are very difficult to 
> canonize a graph?

As I recall, handling chirality and other non-local properties is difficult. I 
have not worked on this problem.

Cheers,

                                Andrew
                                [email protected]




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