稀疏图的(0,1)-松弛强边着色

On(0,1)-relaxed Strong Edge-coloring of Sparse Graphs

给定一个图G=(V (G),E (G)),图G的(s,t)-松弛强边着色数是指使得图G有(s,t)-松弛强k边着色的最小k值,记作χ′(s,t)(G).证明了在图G中,如果mad (G)<3,Δ≤7,那么χ′(0,1)(G)≤3Δ-1;同时证明了对于任意一个平面图G,如果g (G)≥7,Δ≥4,那么χ′(0,1)(G)≤{5Δ/2}.

Let G =( V( G), E( G)) be a graph. The( s, t)-relaxed strong chromatic index, denoted by χ′(s,t)( G), is the minimum number k for which G has an( s,t)-relaxed strong k-edge-coloring. It’s proved that if G is a graph with mad(G) < 3 and Δ≤7, then χ′(s,t)( G)≤3Δ-1. In addition, if G is a planar graph with mad( G) < 3 and Δ≤7, then χ′(s,t)( G)≤{5Δ/2}.