A Characterization on the Adjacent Vertex Distinguishing Index of Planar Graphs with Large Maximum Degree

2015 ◽  
Vol 29 (4) ◽  
pp. 2412-2431 ◽  
Author(s):  
Weifan Wang ◽  
Danjun Huang
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Adjacent Vertex ◽  
Large Maximum

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

Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 8

2020 ◽  
Vol 343 (10) ◽  
pp. 112014
Author(s):  
Yulin Chang ◽  
Jie Hu ◽  
Guanghui Wang ◽  
Xiaowei Yu
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Total Coloring ◽  
Adjacent Vertex

(2,1)-total labelling of planar graphs with large maximum degree

2017 ◽  
Vol 20 (8) ◽  
pp. 1625-1636
Author(s):  
Yong Yu ◽  
Xin Zhang ◽  
Guanghui Wang ◽  
Guizhen Liu ◽  
Jinbo Li
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Large Maximum

scholarly journals Total colorings of planar graphs with large maximum degree

1997 ◽  
Vol 26 (1) ◽  
pp. 53-59 ◽  
Author(s):  
O. V. Borodin ◽  
A. V. Kostochka ◽  
D. R. Woodall
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Large Maximum

scholarly journals Clustered 3-colouring graphs of bounded degree

2021 ◽  
pp. 1-13
Author(s):  
Vida Dujmović ◽  
Louis Esperet ◽  
Pat Morin ◽  
Bartosz Walczak ◽  
David R. Wood
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bounded Degree ◽  
Bounded Number ◽  
Proper Vertex ◽  
Vertex Colouring

Abstract A (not necessarily proper) vertex colouring of a graph has clustering c if every monochromatic component has at most c vertices. We prove that planar graphs with maximum degree $\Delta$ are 3-colourable with clustering $O(\Delta^2)$ . The previous best bound was $O(\Delta^{37})$ . This result for planar graphs generalises to graphs that can be drawn on a surface of bounded Euler genus with a bounded number of crossings per edge. We then prove that graphs with maximum degree $\Delta$ that exclude a fixed minor are 3-colourable with clustering $O(\Delta^5)$ . The best previous bound for this result was exponential in $\Delta$ .

scholarly journals Adjacent vertex distinguishing indices of planar graphs without 3-cycles

2015 ◽  
Vol 338 (3) ◽  
pp. 139-148 ◽  
Author(s):  
Danjun Huang ◽  
Zhengke Miao ◽  
Weifan Wang
Keyword(s):  
Planar Graphs ◽  
Adjacent Vertex
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