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Scholars Journal of Physics, Mathematics and Statistics | Volume-5 | Issue-05
Vertex Arboricity of Planar Graphs without 5-Cycles Intersecting With 6-Cycles
Hongling Chen, Wenshun Teng, Huijuan Wang, Hongwei Gao
Published: Oct. 30, 2018 | 119 72
DOI: 10.21276/sjpms.2018.5.5.7
Pages: 322-327
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Abstract
The vertex arboricity of graph, denoted by va G   , is the minimum number of forest required to partition the vertex set, which is an improper edge coloring. In this paper, we mainly studied vertex arboricity on planar graphs and we have proved if there is without 5 -cycles intersecting with 6 - cycles, then va G    2 . Keywords: Planar graph, vertex arboricity, intersecting, cycles.