Distance constrained labelings of K4K4-minor free graphs

Motivated by previous results on distance constrained labelings and coloring of squares of K4K4-minor free graphs, we show that for every p≥q≥1p≥q≥1, there exists Δ0Δ0 such that every K4K4-minor free graph GG with maximum degree Δ≥Δ0Δ≥Δ0 has an L(p,q)L(p,q)-labeling of span at most q⌊3Δ(G)/2⌋q⌊3Δ(G)/2⌋. The obtained bound is the best possible.