scholarly journals On the vertex-arboricity of planar graphs without 7-cycles

2012 ◽  
Vol 312 (15) ◽  
pp. 2304-2315 ◽  
Author(s):  
Danjun Huang ◽  
Wai Chee Shiu ◽  
Weifan Wang
Keyword(s):  
Planar Graphs ◽  
Vertex Arboricity

Vertex arboricity of planar graphs without intersecting 5-cycles

2017 ◽  
Vol 35 (2) ◽  
pp. 365-372 ◽  
Author(s):  
Hua Cai ◽  
Jianliang Wu ◽  
Lin Sun
Keyword(s):  
Planar Graphs ◽  
Vertex Arboricity

A note of vertex arboricity of planar graphs without 4-cycles intersecting with 6-cycles

2020 ◽  
Vol 836 ◽  
pp. 53-58
Author(s):  
Xuyang Cui ◽  
Wenshun Teng ◽  
Xing Liu ◽  
Huijuan Wang
Keyword(s):  
Planar Graphs ◽  
Vertex Arboricity

scholarly journals On the vertex-arboricity of planar graphs

2008 ◽  
Vol 29 (4) ◽  
pp. 1064-1075 ◽  
Author(s):  
André Raspaud ◽  
Weifan Wang
Keyword(s):  
Planar Graphs ◽  
Vertex Arboricity

scholarly journals Vertex-arboricity of planar graphs without intersecting triangles

2012 ◽  
Vol 33 (5) ◽  
pp. 905-923 ◽  
Author(s):  
Min Chen ◽  
André Raspaud ◽  
Weifan Wang
Keyword(s):  
Planar Graphs ◽  
Vertex Arboricity

Vertex arboricity of graphs embedded in a surface of non-negative Euler characteristic

2020 ◽  
Vol 12 (06) ◽  
pp. 2050080
Author(s):  
Wenshun Teng ◽  
Huijuan Wang
Keyword(s):  
Euler Characteristic ◽  
Planar Graphs ◽  
Quadrilateral Mesh ◽  
Color Class ◽  
Vertex Arboricity ◽  
Minimum Number ◽  
Acyclic Subgraph

The vertex arboricity [Formula: see text] of a graph [Formula: see text] is the minimum number of colors the vertices of the graph [Formula: see text] can be colored so that every color class induces an acyclic subgraph of [Formula: see text]. There are many results on the vertex arboricity of planar graphs. In this paper, we replace planar graphs with graphs which can be embedded in a surface [Formula: see text] of Euler characteristic [Formula: see text]. We prove that for the graph [Formula: see text] which can be embedded in a surface [Formula: see text] of Euler characteristic [Formula: see text] if no [Formula: see text]-cycle intersects a [Formula: see text]-cycle, or no [Formula: see text]-cycle intersects a [Formula: see text]-cycle, then [Formula: see text] in addition to the [Formula: see text]-regular quadrilateral mesh.

scholarly journals On the vertex arboricity of planar graphs of diameter two

2007 ◽  
Vol 307 (19-20) ◽  
pp. 2438-2447 ◽  
Author(s):  
Yang Aifeng ◽  
Yuan Jinjiang
Keyword(s):  
Planar Graphs ◽  
Vertex Arboricity
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