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 ∆0 such that every K4-minor free graph G with maximum degree ∆ ≥ ∆0 has an L(p, q)-labeling of span at most q⌊3∆(G)/2⌋. The obtained bound is the best possible.

Distance constrained labelings of K4-minor free graphs

AbstractMotivated 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(G)/2⌋. The obtained bound is the best possible