给定两个非负整数s和t，图G的(s，t)-松弛强k边着色可表示为映射c：E(G)→[k]，这个映射满足对G中的任意一条边e，颜色c(e)在e的1-邻域中最多出现s次并且在e的2-邻域中最多出现t次。图G的(s，t)-松弛强边着色指数，记作χ'_(s，t)(G)，表示使得图G有(s，t)-松弛强k边着色的最小k值。在图G中，如果mad(G) < 3并且Δ≤4，那么χ'_(1，0)(G)≤3Δ。并证明如果G是平面图，最大度Δ≥4并且围长最少为7，那么χ'_(1，0)(G)≤3Δ-1。

Let G be a graph. For two nonnegative integers s and t, an (s, t)-relaxed strong k-edge-coloring is a mapping c : E(G) → [k], such that for any edge e, there are at most s edges adjacent to e and t edges which are distance two apart from e having the color c(e). The (s, t)-relaxed strong chromatic index, denoted by χ' (s, t)(G), is the minimum number k such that G admits an (s, t)-relaxed strong k-edge-coloring. We prove that if G is a graph with mad(G) < 3 and Δ ≤ 4, then χ'_{(1, 0)}(G) ≤ 3Δ. In addition, we prove that if G is a planar graph with Δ ≥ 4 and girth at least 7, then χ'_{(1, 0)}(G) ≤ 3Δ - 1.