A self-stabilizing ()-edge-coloring algorithm for planar graphs in anonymous uniform systems

2007 ◽  
Vol 101 (4) ◽  
pp. 168-173 ◽  
Author(s):  
Chi-Hung Tzeng ◽  
Jehn-Ruey Jiang ◽  
Shing-Tsaan Huang
Keyword(s):  
Planar Graphs ◽  
Edge Coloring

scholarly journals Acyclic edge coloring conjecture is true on planar graphs without intersecting triangles

2021 ◽  
Author(s):  
Qiaojun Shu ◽  
Yong Chen ◽  
Shuguang Han ◽  
Guohui Lin ◽  
Eiji Miyano ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
Acyclic Edge Coloring

Adjacent vertex distinguishing edge coloring of planar graphs without 3-cycles

2020 ◽  
Vol 12 (04) ◽  
pp. 2050035
Author(s):  
Danjun Huang ◽  
Xiaoxiu Zhang ◽  
Weifan Wang ◽  
Stephen Finbow
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Edge Coloring ◽  
Discrete Math ◽  
Adjacent Vertex ◽  
Chromatic Index ◽  
Proper Edge Coloring ◽  
Minimum Number

The adjacent vertex distinguishing edge coloring of a graph [Formula: see text] is a proper edge coloring of [Formula: see text] such that the color sets of any pair of adjacent vertices are distinct. The minimum number of colors required for an adjacent vertex distinguishing edge coloring of [Formula: see text] is denoted by [Formula: see text]. It is observed that [Formula: see text] when [Formula: see text] contains two adjacent vertices of degree [Formula: see text]. In this paper, we prove that if [Formula: see text] is a planar graph without 3-cycles, then [Formula: see text]. Furthermore, we characterize the adjacent vertex distinguishing chromatic index for planar graphs of [Formula: see text] and without 3-cycles. This improves a result from [D. Huang, Z. Miao and W. Wang, Adjacent vertex distinguishing indices of planar graphs without 3-cycles, Discrete Math. 338 (2015) 139–148] that established [Formula: see text] for planar graphs without 3-cycles.

Acyclic Edge Coloring of IC-planar Graphs

2020 ◽  
Vol 36 (3) ◽  
pp. 581-589
Author(s):  
Wen-yao Song ◽  
Yuan-yuan Duan ◽  
Juan Wang ◽  
Lian-ying Miao
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
Acyclic Edge Coloring

scholarly journals Acyclic edge coloring of planar graphs with large girth

2009 ◽  
Vol 410 (47-49) ◽  
pp. 5196-5200 ◽  
Author(s):  
Dongxiao Yu ◽  
Jianfeng Hou ◽  
Guizhen Liu ◽  
Bin Liu ◽  
Lan Xu
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
Acyclic Edge Coloring ◽  
Large Girth

Edge coloring of planar graphs without adjacent 7-cycles

2018 ◽  
Vol 739 ◽  
pp. 59-64 ◽  
Author(s):  
Wenwen Zhang ◽  
Jian-Liang Wu
Keyword(s):  
Planar Graphs ◽  
Edge Coloring

List strong edge coloring of planar graphs with maximum degree 4

2019 ◽  
Vol 342 (5) ◽  
pp. 1471-1480
Author(s):  
Ming Chen ◽  
Jie Hu ◽  
Xiaowei Yu ◽  
Shan Zhou
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Edge Coloring

New Linear-Time Algorithms for Edge-Coloring Planar Graphs

Algorithmica ◽  
2007 ◽  
Vol 50 (3) ◽  
pp. 351-368 ◽  
Author(s):  
Richard Cole ◽  
Łukasz Kowalik
Keyword(s):  
Planar Graphs ◽  
Linear Time ◽  
Edge Coloring ◽  
Linear Time Algorithms
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