不含相交三角形平面图无圈边染色

Acyclic Edge Coloring of Planar Graphs Without Intersecting Triangles

如果图G的正常边染色不包含2-色圈,则称它是图G的一个无圈边染色.图G的无圈边色数表示图G的无圈边染色所需的最小颜色数.为研究平面图的无圈边色数的上界,利用差值转移方法并结合平面图的结构性质,证明了不含相交三角形的平面图的无圈边色数不超过Δ(G)+7.

Given that a proper edge coloring of G contains no bichromatic cycles inG,then it is an acyclic edge coloring of G.The acyclic chromatic number of G is the minimum number of colors among all the acyclic edge colorings of G.In order to study the upper bound of acyclic chromatic number of planar graphs,by using discharging methods and some properties of planar graphs,the paper has proved that if G is a planar graph without intersecting triangles,then its acyclic chromatic number will be not more than G.