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Fix typos in markdown and comments (#32)
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Lectures/sparse.jl

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@@ -62,7 +62,7 @@ md"## The same applies to reverse mode"
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md"# Sparsity detection of Jacobian"
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# ╔═╡ 0a91e27f-3cea-415e-aed4-123482da375a
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md"Simple [operator overleading implementation](https://adrianhill.de/SparseConnectivityTracer.jl/dev/internals/how_it_works/)"
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md"Simple [operator overloading implementation](https://adrianhill.de/SparseConnectivityTracer.jl/dev/internals/how_it_works/)"
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# ╔═╡ 97c94c5a-fab5-4226-b803-10c85a298f2a
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struct MyGradientTracer
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Given a graph ``G(V,E)``,
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* Nodes ``u, v`` are distance ``k`` neighbors if there exists a path from ``u`` to ``v`` of length at most ``k``.
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* A *distance-*``k`` coloring : mapping ``\phi:V \to \{1, \ldots, p\}`` such that ``\phi(u) \neq \phi(v)`` whenever ``u, v`` are distance-``k`` neighbors.
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* ``k``*-chromatic number* ``\xi_k(G)`` : mininum ``p`` such that ``\exists`` distance-``k`` coloring with ``p`` colors.
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* ``k``*-chromatic number* ``\xi_k(G)`` : minimum ``p`` such that ``\exists`` distance-``k`` coloring with ``p`` colors.
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* Distance-``k`` coloring problem : Find distance-``k`` coloring with fewest colors.
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* For every fixed integer ``k \ge 1``, the distance-``k`` graph coloring problem [is NP-hard](https://doi.org/10.1137/S089548019120016X).
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