The Linear Arboricity of Planar Graphs with Maximum Degree at Least Five

被引：0

作者：

Tan, Xiang ^{[1
,3
]}

Chen, Hongyu ^{[2
,3
]}

Wu, Jianliang ^{[3
]}

机构：

[1] Shandong Univ Finance, Sch Math & Stat, Jinan 250014, Shandong, Peoples R China

[2] Shanghai Inst Technol, Sch Sci, Shanghai 201418, Peoples R China

[3] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2011年 / 34卷 / 03期

关键词：

Planar graph; linear arboricity; cycle; PACKING;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a planar graph with maximum degree Delta >= 5. It is proved that la(G) = inverted right perpendicular Delta(G)/2inverted left perpendicular if (1) any 4-cycle is not adjacent to an i-cycle for any i is an element of {3,4, 5} or (2) G has no intersecting 4-cycles and intersecting i-cycles for some i is an element of {3, 6}.

引用

页码：541 / 552

页数：12

共 16 条

[1]

Akiyama J., 1980, Mathematica Slovaca, V30, P405

[2] COVERING AND PACKING IN GRAPHS .4. LINEAR ARBORICITY [J].

AKIYAMA, J ;

EXOO, G ;

HARARY, F .

NETWORKS, 1981, 11 (01) :69-72

[3]

CHEN HY, LINEAR ARBO IN PRESS

[4] THE LINEAR ARBORICITY OF SOME REGULAR GRAPHS [J].

ENOMOTO, H ;

PEROCHE, B .

JOURNAL OF GRAPH THEORY, 1984, 8 (02) :309-324

[5]

Gulden F., 1986, Mathematica Slovaca, V36, P225

[6] COVERING AND PACKING IN GRAPHS, .1. [J].

HARARY, F .

ANNALS OF THE NEW YORK ACADEMY OF SCIENCES, 1970, 175 (01) :198-&

[7]

Jianliang Wu, 2002, Journal of Systems Science and Complexity, V15, P372

[8]

Wu J.L., LINEAR ARBORIC UNPUB

[9] The linear arboricity of planar graphs of maximum degree seven is four [J].

Wu, Jian-Liang ;

Wu, Yu-Wen .

JOURNAL OF GRAPH THEORY, 2008, 58 (03) :210-220

[10] The linear arboricity of planar graphs with no short cycles [J].

Wu, Jian-Liang ;

Hou, Jian-Feng ;

Liu, Gui-Zhen .

THEORETICAL COMPUTER SCIENCE, 2007, 381 (1-3) :230-233

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