Odd coloring graphs with linear neighborhood complexity
By: James Davies , Meike Hatzel , Kolja Knauer and more
Potential Business Impact:
Makes some tricky math problems easier to solve.
We prove that any class of bipartite graphs with linear neighborhood complexity has bounded odd chromatic number. As a result, if $\mathcal{G}$ is the class of all circle graphs, or if $\mathcal{G}$ is any class with bounded twin-width, bounded merge-width, or a forbidden vertex-minor, then $\mathcal{G}$ is $\chi_{odd}$-bounded.
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