Distance Constrained Labelings of K4-minor Free Graphs

Motivated by previous results on distance constrained labelings and coloring of squares of K4-minor free graphs, we show that for every p⩾q⩾1, there exists Δ0 such that every K4-minor free graph G with maximum degree Δ⩾Δ0 has an L(p,q)-labeling of span at most q⌊3Δ/2⌋. The obtained bound is the best possible.