Discrete Mathematics, Algorithms and Applications, 2021 (Refereed Journals of Other Institutions)
© World Scientific Publishing Company.We find sufficient conditions for the square of a comparability graph Comp(P) of a poset P to be (Δ + r)-colorable when Comp(P) lacks K2,r for some r ≥ 1. 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.