Total colorings-a survey

被引：4
|
作者：
Geetha, Jayabalan [1 ]
Narayanan, Narayanan [2 ]
Somasundaram, Kanagasabapathi [1 ]
机构：
[1] Coimbatore Amrita Vishwa Vidyapeetham, Dept Math, Amrita Sch Phys Sci, Ettimadai, India
[2] Indian Inst Technol Madras, Dept Math, Chennai, India
来源：
AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS | 2023年 / 20卷 / 03期
关键词：
Total coloring; survey; planar graph; product graphs; non-planar graphs; TOTAL-CHROMATIC NUMBER; COMPLETE MULTIPARTITE GRAPHS; LIST TOTAL COLORINGS; MAXIMUM DEGREE 6; PLANAR GRAPHS; REGULAR GRAPHS; DIRECT-PRODUCT; EDGE; ADJACENT; VERTEX;
D O I：
10.1080/09728600.2023.2187960
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The smallest integerkneeded for the assignment ofkcolors to the elements so that the coloringis proper (vertices and edges) is called the total chromatic number of a graph. Vizing [126] andBehzad [6,7] conjectured that the total coloring can be done using at most delta(G) + 2 colors,where delta(G) is the maximum degree ofG. It is not settled even for planar graphs. In this paper,we give a survey on the total coloring of graphs.
引用
收藏
页码：339 / 351
页数：13
相关论文
共 50 条
  • [31] Total Colorings of Planar Graphs without Small Cycles
    Jianfeng Hou
    Yan Zhu
    Guizhen Liu
    Jianliang Wu
    Mei Lan
    Graphs and Combinatorics, 2008, 24 : 91 - 100
  • [32] NEIGHBOR PRODUCT DISTINGUISHING TOTAL COLORINGS OF PLANAR GRAPHS WITH MAXIMUM DEGREE AT LEAST TEN
    Dong, Aijun
    Li, Tong
    DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2021, 41 (04) : 981 - 999
  • [33] Total colorings of planar graphs with maximum degree at least 8
    Lan Shen
    YingQian Wang
    Science in China Series A: Mathematics, 2009, 52 : 1733 - 1742
  • [34] Total colorings of planar graphs with maximum degree at least 8
    SHEN Lan & WANG YingQian College of Mathematics
    Science China Mathematics, 2009, (08) : 1733 - 1742
  • [35] Acyclic Total Colorings of Planar Graphs
    Sun, Xiang Yong
    Wu, Jian Liang
    ARS COMBINATORIA, 2015, 123 : 269 - 282
  • [36] Neighbor Sum Distinguishing Total Colorings of Corona of Subcubic Graphs
    Dong, Aijun
    Zhang, Wenwen
    Tan, Xiang
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (04) : 1919 - 1926
  • [37] Total-colorings of complete multipartite graphs using amalgamations
    Dalal, Aseem
    Panda, B. S.
    Rodger, C. A.
    DISCRETE MATHEMATICS, 2016, 339 (05) : 1587 - 1592
  • [38] GENERALIZED FRACTIONAL TOTAL COLORINGS OF GRAPHS
    Karafova, Gabriela
    Sotak, Roman
    DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2015, 35 (03) : 463 - 473
  • [39] Total colorings of planar graphs without intersecting 4-cycles and intersecting 5-cycles
    Tan, Xiang
    Chen, Hong-Yu
    UTILITAS MATHEMATICA, 2017, 104 : 141 - 150
  • [40] Total colorings of planar graphs with maximum degree 8 and without 5-cycles with two chords
    Chang, Jian
    Wang, Hui-Juan
    Wu, Jian-Liang
    A, Yong-Ga
    THEORETICAL COMPUTER SCIENCE, 2013, 476 : 16 - 23
12345