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Decomposing a planar graph with girth at least 8 into a forest and a matching

机译:将周长至少为8的平面图分解为森林并进行匹配

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摘要

W. He et al. showed that a planar graph of girth at least 11 can be decomposed into a forest and a matching. A. Bass et al. proved the same statement for planar graphs of girth at least 10. Recently, O.V. Borodin et al. improved the bound on the girth to 9. In this paper, we further improve the bound on the girth to 8. This bound is the best possible in the sense that there are planar graphs with girth 7 that cannot be decomposed into a forest and a matching.
机译:W.He等。结果表明,至少有11个围的平面图可以分解为一个森林和一个匹配项。 A.巴斯等。证明至少有10个周长的平面图具有相同的陈述。 Borodin等。将周长的界线提高到9。在本文中,我们进一步将周长的界线提高到8。从某种意义上说,此界线是最好的,因为有些平面图的周长7不能分解为森林和匹配。

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