Abstract
We find sufficient conditions for the square of a comparability graph [Formula: see text] of a poset [Formula: see text] to be [Formula: see text]-colorable when [Formula: see text] lacks [Formula: see text] for some [Formula: see text]. Furthermore, we show that the problem of coloring the square of the comparability graph of a poset of height at least four can be reduced to the case of height three, where the height of a poset is the size of a maximum chain.
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