scholarly journals Total-Coloring of Plane Graphs with Maximum Degree Nine

2008 ◽  
Vol 22 (4) ◽  
pp. 1462-1479 ◽  
Author(s):  
Łukasz Kowalik ◽  
Jean-Sébastien Sereni ◽  
Riste Škrekovski
Keyword(s):  
Maximum Degree ◽  
Total Coloring ◽  
Plane Graphs

Plane graphs of maximum degree Δ ≥ 7 are edge‐face (Δ + 1)‐colorable

2020 ◽  
Vol 95 (1) ◽  
pp. 99-124
Author(s):  
Yiqiao Wang ◽  
Xiaoxue Hu ◽  
Weifan Wang ◽  
Ko‐Wei Lih
Keyword(s):  
Maximum Degree ◽  
Plane Graphs

Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 9

2019 ◽  
Vol 342 (5) ◽  
pp. 1392-1402
Author(s):  
Jie Hu ◽  
Guanghui Wang ◽  
Jianliang Wu ◽  
Donglei Yang ◽  
Xiaowei Yu
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Total Coloring ◽  
Adjacent Vertex

scholarly journals Total Coloring Conjecture for Certain Classes of Graphs

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 161 ◽  
Author(s):  
R. Vignesh ◽  
J. Geetha ◽  
K. Somasundaram
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Line Graph ◽  
Product Line ◽  
Total Coloring ◽  
Lexicographic Product ◽  
Total Chromatic Number ◽  
Minimum Number ◽  
Total Coloring Conjecture

A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements receive the same color. The total chromatic number of a graph G, denoted by χ ′ ′ ( G ) , is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, Δ ( G ) + 1 ≤ χ ′ ′ ( G ) ≤ Δ ( G ) + 2 , where Δ ( G ) is the maximum degree of G. In this paper, we prove the total coloring conjecture for certain classes of graphs of deleted lexicographic product, line graph and double graph.

Total colorings of circulant graphs

2020 ◽  
pp. 2150050
Author(s):  
J. Geetha ◽  
K. Somasundaram ◽  
Hung-Lin Fu
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Total Coloring ◽  
Circulant Graphs ◽  
Total Chromatic Number ◽  
Number Formula ◽  
Total Coloring Conjecture

The total chromatic number [Formula: see text] is the least number of colors needed to color the vertices and edges of a graph [Formula: see text] such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): [Formula: see text], where [Formula: see text] is the maximum degree of [Formula: see text]. For the powers of cycles, Campos and de Mello proposed the following conjecture: Let [Formula: see text] denote the graphs of powers of cycles of order [Formula: see text] and length [Formula: see text] with [Formula: see text]. Then, [Formula: see text] In this paper, we prove the Campos and de Mello’s conjecture for some classes of powers of cycles. Also, we prove the TCC for complement of powers of cycles.

EDGE-FACE CHROMATIC NUMBER OF 2-CONNECTED PLANE GRAPHS WITH HIGH MAXIMUM DEGREE

2006 ◽  
Vol 26 (3) ◽  
pp. 477-482
Author(s):  
Zhongfu Zhang ◽  
Weifan Wang ◽  
Jingwen Li ◽  
Bing Yao ◽  
Yuehua Bu
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Plane Graphs ◽  
High Maximum

scholarly journals Total coloring of embedded graphs with maximum degree at least seven

2014 ◽  
Vol 518 ◽  
pp. 1-9 ◽  
Author(s):  
Huijuan Wang ◽  
Bin Liu ◽  
Jianliang Wu ◽  
Guizhen Liu
Keyword(s):  
Maximum Degree ◽  
Total Coloring ◽  
Embedded Graphs

Plane Graphs with Maximum Degree Δ≥8 Are Entirely (Δ+3)-Colorable

2012 ◽  
Vol 73 (3) ◽  
pp. 305-317 ◽  
Author(s):  
Yingqian Wang ◽  
Xianghua Mao ◽  
Zhengke Miao
Keyword(s):  
Maximum Degree ◽  
Plane Graphs

scholarly journals Plane graphs with maximum degree 9 are entirely 11-choosable

2016 ◽  
Vol 339 (11) ◽  
pp. 2742-2753
Author(s):  
Xiaoxue Hu ◽  
Weifan Wang ◽  
Wai Chee Shiu ◽  
Yiqiao Wang
Keyword(s):  
Maximum Degree ◽  
Plane Graphs

Plane graphs with maximum degree 7 and without 5-cycles with chords are 8-totally-colorable

2011 ◽  
Vol 41 (1) ◽  
pp. 95-104 ◽  
Author(s):  
Qiang SUN ◽  
Xin SHEN Lan TAO ◽  
岚 沈 ◽  
YingQian WANG
Keyword(s):  
Maximum Degree ◽  
Plane Graphs
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