无4,5,6-圈且无两个相交三角形的平面图的L(p,q)-标号

J4 ›› 2013, Vol. 48 ›› Issue (4): 28-34.

无4,5,6-圈且无两个相交三角形的平面图的L(p,q)-标号

朱海洋1,陈伟1,吕新忠2,李培君3

1.空军勤务学院飞行保障指挥系, 江苏徐州 221000; 2.浙江师范大学数理与信息工程学院, 浙江金华 321004;
3.空军勤务学院机场工程系, 江苏徐州 221000

收稿日期:2011-05-08 出版日期:2013-04-20 发布日期:2013-04-16
作者简介:朱海洋(1979- ),男,硕士,讲师,研究方向为图论与军事运筹学. Email:tulunzhuhaiyang7@126.com
基金资助:
国家自然科学基金资助项目(10971198)

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

ZHU Hai-yang1, CHEN Wei1, L Xin-zhong2, LI Pei-jun3

1. Department of Flight Support, Air Force Logistical College, Xuzhou 221000, Jiangsu, China;
2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University,
Jinhua 321004, Zhejiang, China;
3.Department of Airport Engineering, Air Force Logistical College, Xuzhou 221000, Jiangsu, China

Received:2011-05-08 Online:2013-04-20 Published:2013-04-16

摘要/Abstract

摘要：

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。

关键词: L(p,q)-标号;平面图;圈

Abstract:

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.

Key words: L(p,q)-labeling; planar graph; cycles

朱海洋1,陈伟1,吕新忠2,李培君3. 无4,5,6-圈且无两个相交三角形的平面图的L(p,q)-标号[J]. J4, 2013, 48(4): 28-34.

ZHU Hai-yang1, CHEN Wei1, L Xin-zhong2, LI Pei-jun3. On L(p,q)-labeling of planar graphs without 4,5,6-cycles and intersecting triangles[J]. J4, 2013, 48(4): 28-34.

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