The Linear Arboricity of Planar Graphs without 5-, 6-Cycles with Chords

2011 ◽  
Vol 29 (3) ◽  
pp. 373-385 ◽  
Author(s):  
Hongyu Chen ◽  
Xiang Tan ◽  
Jianliang Wu ◽  
Guojun Li
Keyword(s):  
Planar Graphs ◽  
Linear Arboricity

The linear arboricity of planar graphs of maximum degree seven is four

2008 ◽  
Vol 58 (3) ◽  
pp. 210-220 ◽  
Author(s):  
Jian-Liang Wu ◽  
Yu-Wen Wu
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Linear Arboricity

List linear arboricity of planar graphs

2009 ◽  
Vol 29 (3) ◽  
pp. 499 ◽  
Author(s):  
Xinhui An ◽  
Baoyindureng Wu
Keyword(s):  
Planar Graphs ◽  
Linear Arboricity

scholarly journals The linear arboricity of planar graphs with no short cycles

2007 ◽  
Vol 381 (1-3) ◽  
pp. 230-233 ◽  
Author(s):  
Jian-Liang Wu ◽  
Jian-Feng Hou ◽  
Gui-Zhen Liu
Keyword(s):  
Planar Graphs ◽  
Linear Arboricity

scholarly journals The linear arboricity of planar graphs without 5-cycles with two chords

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1135-1142 ◽  
Author(s):  
Xiang-Lian Chen ◽  
Jian-Liang Wu
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Linear Arboricity ◽  
Minimum Number

The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. In this paper, it is proved that for a planar graph G,la(G)=?(?(G)/2)? if ?(G) ? 7 and G has no 5-cycles with two chords.

The structure of plane graphs with independent crossings and its applications to coloring problems

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Xin Zhang ◽  
Guizhen Liu
Keyword(s):  
Planar Graph ◽  
Chromatic Number ◽  
Planar Graphs ◽  
Maximum Degree ◽  
Minimum Degree ◽  
Plane Graph ◽  
Plane Graphs ◽  
Total Chromatic Number ◽  
Linear Arboricity

AbstractIf a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is Δ if Δ ≥ 8, the list edge (resp. list total) chromatic number of G is Δ (resp. Δ + 1) if Δ ≥ 14 and the linear arboricity of G is ℈Δ/2⌊ if Δ ≥ 17, where G is an IC-planar graph and Δ is the maximum degree of G.

scholarly journals On point-linear arboricity of planar graphs

1988 ◽  
Vol 72 (1-3) ◽  
pp. 381-384 ◽  
Author(s):  
Jianfang Wang
Keyword(s):  
Planar Graphs ◽  
Linear Arboricity
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