The linear arboricity of upper-embedded graph and secondary upper-embedded graph

LYU Chang-Qing

doi:10.3969/j.issn.1000-5641.2015.01.016

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Mar. 2015

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LYU Chang-Qing. The linear arboricity of upper-embedded graph and secondary upper-embedded graph[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 131-135. doi: 10.3969/j.issn.1000-5641.2015.01.016

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LYU Chang-Qing. The linear arboricity of upper-embedded graph and secondary upper-embedded graph[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 131-135. doi: 10.3969/j.issn.1000-5641.2015.01.016

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The linear arboricity of upper-embedded graph and secondary upper-embedded graph

doi: 10.3969/j.issn.1000-5641.2015.01.016

LYU Chang-Qing^,

1.
School of Mathematics and Statistics, Zaozhuang University, Zaozhuang Shandong, 277160, China

Received Date: 2014-04-01
Publish Date: 2015-01-25

Abstract

Abstract

The linear arboricity of a graph $G$ is the minimum number of linear forests which partition the edges of $G$. In the present, it is proved that if a upper-embedded graph $G$ has $\Delta\geqslant 3\sqrt{4-3\varepsilon}$ then its linear arboricity is $\lceil\frac{\Delta}{2}\rceil$\,and if a secondary upper-embedded graph $G$ has $\Delta\geqslant 6\sqrt{1-\varepsilon}$ then its linear arboricity is $\lceil \frac{\Delta}{2}\rceil$, where $\varepsilon\leqslant0$. It improves the bound of the conclusion in [1]. As its application, the linear arboricity of a triangulation graph on double torus is concluded
- linear arboricity,
- surface,
- (secondary) upper-embedded graph,
- Euler characteristic

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References(1)

References

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