[1]李艳怡,陈莉莉.次立方平面图的单射边染色[J].华侨大学学报(自然科学版),2022,43(3):412-415.[doi:10.11830/ISSN.1000-5013.202010045]
　LI Yanyi,CHEN Lili.Injective Edge Coloring of Planar Subcubic Graphs[J].Journal of Huaqiao University(Natural Science),2022,43(3):412-415.[doi:10.11830/ISSN.1000-5013.202010045]
点击复制

次立方平面图的单射边染色()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第43卷
期数:
2022年第3期
页码:
412-415
栏目:
出版日期:
2022-05-10

文章信息/Info

Title:
Injective Edge Coloring of Planar Subcubic Graphs
文章编号:
1000-5013(2022)03-0412-04
作者:
李艳怡;  陈莉莉
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
LI Yanyi;  CHEN Lili
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
次立方图;  平面图;  围长;  单射边染色
Keywords:
subcubic graph;  planar graph;  girth;  injective edge coloring
分类号:
O157.5
DOI:
10.11830/ISSN.1000-5013.202010045
文献标志码:
A
摘要:
如果3条边e1,e2,e3按照此顺序形成一条长为3的路或者圈,则称这3条边是连续的.k-单射边染色是对图G的边进行染色,使得如果3条边e1,e2,e3是连续的,那么,e1和e3染不同的颜色.图G的单射边色数为所有单射边染色中所用颜色最少的颜色数.文中考虑在限制围长条件下,次立方平面图G的单射边色数.
Abstract:
If three edges e1, e2, e3 form a path or cycle of length three in this order, they are called consecutive. A k-injective edge coloring is a coloring of the edges of G, such that if e1, e2, e3 are consecutive, then e1 and e3 receive distinct colors. The injective edge coloring number is the smallest number of colors used in all injective edge colorings of G. In this paper, we consider the injective edge coloring numbers of the planar subcubic graphs in terms of the girth of G.

参考文献/References:

[1] HAHN G,KRATOCHVíL J,SIRáN J,et al.On the injective chromatic number of graphs[J].Discrete Mathematics,2002,256:179-192.DOI:10.1016/S0012-365X(01)00466-6.
[2] BERTOSSI A A,BONUCCELLI M A.Code assignment for hidden terminal interference avoidance in multihop packet radio networks[J].IEEE/ACM Transactions on Networking,1995,3(4):441-449.DOI:10.1109/90.413218.
[3] CARDOSO D M,CERDEIRA J O,CRUZ J P,et al.Injective edge coloring of graphs[J].Filomat,2019,33(19):6411-6423.DOI:10.2298/FIL1919411C.
[4] BU Yuehua,CHEN Dong,RASPAUD A,et al.Injective coloring of planar graphs[J].Discrete Applied Mathematics,2009,157(4):663-672.DOI:10.1016/j.dam.2008.08.016.
[5] BU Yuehua,LU Kai.Injective coloring of planar graphs with girth 7[J].Discrete Mathematics, Algorithms and Applications,2012,4(2):1250034.DOI:10.1142/S1793830912500346.
[6] 卜月华,叶飘飘.围长至少为5的平面图的injective染色[J].浙江师范大学学报(自然科学版),2017,40(1):1-8.DOI:10.16218/j.issn.1001-5051.2017.01.00.
[7] DONG Wei,LIN Wensong.Injective coloring of planar graphs with girth 6[J].Discrete Mathematics,2013,313:1302-1311.DOI:10.1016/j.disc.2013.02.014.
[8] 朱海洋,王淑玲,刘嫚,等.平面图的单射染色[J].西南师范大学学报(自然科学版),2017,42(4):7-13.DOI:10.13718/j.cnki.xsxb.2017.04.002.
[9] BORODIN O V,IVANOVA A O.List injective colorings of planar graphs[J].Discrete Mathematics,2011,311:154-165.DOI:10.1016/j.disc.2010.10.008.
[10] BU Yuehua,LU Kai.List injective coloring of planar graphs with girth 5, 6, 8[J].Discrete Applied Mathematics,2013,161(10/11):1367-1377.DOI:10.1016/j.dam.2012.12.017.
[11] BU Yuehua,YANG Sheng.List injective coloring of planar graphs with girth g≥5[J].Discrete Mathematics, Algorithms and Applications,2014,6(1):145006.DOI:10.1142/S1793830914500062.
[12] CHEN Hongyu,WU Jianliang.List injective coloring of planar graphs with girth g≥6[J].Discrete Mathematics,2016,339(12):3043-3052.DOI:10.1016/j.disc.2016.06.017.
[13] BRIMKOV B,EDMOND J,LAZAR R,et al.Injective choosability of subcubic planar graphs with girth 6[J].Discrete Mathematics,2017,340(10):2538-2549.DOI:10.1016/j.disc.2017.05.014.
[14] 卜月华,黄超媛. 5--圈和 5--圈不交的平面图的injective-列表染色[J].浙江师范大学学报(自然科学版),2020,43(3):241-250.DOI:10.16218/j.issn.1001-5051.2020.03.001.
[15] BU Yuehua,QI Chentao.Injective edge coloring of sparse graphs[J].Discrete Mathematics, Algorithms and Applications,2018,10(2):1850022.DOI:10.1142/S1793830918500222.
[16] 卜月华,陈雯雯.围长至少是6的平面图的injective-边染色[J].浙江师范大学学报(自然科学版),2020,43(1):19-25.DOI:10.16218/j.issn.1001-5051.2020.01.004.

备注/Memo

备注/Memo:
收稿日期: 2020-10-30
通信作者: 陈莉莉(1986-),女,副教授,博士,主要从事图染色的研究.E-mail:lily60612@126.com.
基金项目: 国家自然科学基金资助项目(11701195); 福建省自然科学基金资助项目(2020J05058)
更新日期/Last Update: 2022-05-20