Strong chromatic index of K4-minor free graphs

The strong chromatic index χs′(G) of a graph G is the smallest integer k such that G has a proper edge k-colouring with the condition that any two edges at distance at most 2 receive distinct colours. In this paper, we prove that if G is a K4-minor free graph with maximum degree Δ≥3, then χs′(G)≤3Δ−2. The result is best possible in the sense that there exist K4-minor free graphs G with maximum degree Δ such that χs′(G)=3Δ−2 for any given integer Δ≥3.