In combinatorially sphere-like ranked posets of rank k where rank-(k-2) elements have even covering degree, the maximal elements admit a proper 2-coloring.
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$2$-colourability of the maximum ranked elements of a combinatorially sphere-like ranked poset
In combinatorially sphere-like ranked posets of rank k where rank-(k-2) elements have even covering degree, the maximal elements admit a proper 2-coloring.