无4,5,6-圈且无两个相交三角形的平面图的L(p,q)-标号

On L(p,q)-labeling of planar graphs without 4,5,6-cycles and intersecting triangles

令λp,q(G)为图G的L(p,q)-标号数,证明了若G是不含4,5,6-圈且不含两个相交三角形的平面图,则λp,q(G)≤(2q-1)Δ(G)+max{4p+4q-4,6p+2q-4,8p-4}。这一结果暗含着对于不含4,5,6-圈且不含两个相交三角形的平面图G,Wegner的猜想成立。

Let λp,q（G） denote the L（p, q）-labeling number of a planar graph G. It is showed that if G be a planar graphs without 4,5,6-cycles and intersecting triangles, then λp,q（G）≤（2q-1）Δ（G）＋max{4p＋4q-4,6p＋2q-4,8p-4}. This result imply that Wagner＇ s conjecture holds for a planar graph G without 4,5,6-cycles and intersecting triangles.