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Improve ChromaticNumber with Brooks' theorem #446

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merged 1 commit into from
Mar 22, 2021
Merged

Improve ChromaticNumber with Brooks' theorem #446

merged 1 commit into from
Mar 22, 2021

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wilfwilson
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@wilfwilson wilfwilson commented Mar 19, 2021 •
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https://en.wikipedia.org/wiki/Brooks'_theorem:

For any connected undirected graph G with maximum degree Δ, the chromatic number of G is at most Δ, unless G is a complete graph or an odd cycle, in which case the chromatic number is Δ + 1

The greedy colouring algorithm can sometimes give Δ + 1 as an upper bound (and maybe more?) when Brooks' theorem gives us just Δ. So let's take the minimum of the two in ChromaticNumber.

@wilfwilson wilfwilson added performance A label for issues or PR related to performance minor A label for PRs or issues that are minor in some sense. labels Mar 19, 2021
@wilfwilson wilfwilson force-pushed the better-chromatic-number-upper-bound branch from 78eb458 to bf9aab0 Compare March 19, 2021 17:13
@wilfwilson wilfwilson added the merge-in-to-master A label for PRs that should be merged into the master branch label Mar 19, 2021
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This could be merged into stable-1.4, since I don't think it adds any new features.

@wilfwilson wilfwilson force-pushed the better-chromatic-number-upper-bound branch from bf9aab0 to 36780da Compare March 22, 2021 10:42
@wilfwilson wilfwilson changed the base branch from master to stable-1.4 March 22, 2021 10:42
@wilfwilson wilfwilson removed the merge-in-to-master A label for PRs that should be merged into the master branch label Mar 22, 2021
@wilfwilson wilfwilson force-pushed the better-chromatic-number-upper-bound branch from 36780da to 80b36bc Compare March 22, 2021 10:48
@wilfwilson wilfwilson merged commit 249d25f into digraphs:stable-1.4 Mar 22, 2021
@wilfwilson wilfwilson deleted the better-chromatic-number-upper-bound branch March 22, 2021 11:54
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