不含3-,4-,7-圈平面图的2-距离染色  

2-distance coloring of planar graphs without 3-, 4-, 7-cycles

作　　者：卜月华[1,2] 包智敏 朱洪国 BU Yuehua;BAO Zhimin;ZHU Hongguo(School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,China;Department of Basics,Zhejiang Guangsha Vocational and Technical University of Construction,Dongyang 322100,China)

机构地区：[1]浙江师范大学数学科学学院,浙江金华321004 [2]浙江广厦建设职业技术大学基础部,浙江东阳322100

出　　处：《浙江师范大学学报(自然科学版)》2025年第2期133-141,共9页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(12031018,12201569)。

摘　　要：通过分析极小反例平面图的结构性质,并运用权转移技巧,研究了不含3-,4-,7-圈平面图的2-距离色数.证明了Δ≥24且无3-,4-,7-圈的平面图G,有χ_(2)(G)≤Δ+3.该研究结果推广了此类平面图的2-距离染色的已知结果.It was studied the 2-distance chromatic number of planar graphs without 3-,4-,7-cycles,by analyzing the structural properties of the minimal counterexample and applying the discharging method.It was proved that every planar graph withΔ≥24 and without 3-,4-,7-cycles could be(Δ+3)-2-distance colorable.The presented results generalized the relevant known results of 2-distance coloring of such graphs.

关 键 词：平面图 2-距离染色 圈 权转移 

分 类 号：O157.5[理学—数学]