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arXiv · 1903.08337

Equitable partition of plane graphs with independent crossings into induced forests

Bei Niu·Xin Zhang·Yuping Gao
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Abstract

The cluster of a crossing in a graph drawing in the plane is the set of the four end-vertices of its two crossed edges. Two crossings are independent if their clusters do not intersect. In this paper, we prove that every plane graph with independent crossings has an equitable partition into $m$ induced forests for any $m\geq 8$. Moreover, we decrease this lower bound 8 for $m$ to 6, 5, 4 and 3 if we additionally assume that the girth of the considering graph is at least 4, 5, 6 and 26, respectively.

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Bei Niu, Xin Zhang, Yuping Gao. 2019-12-16. Equitable partition of plane graphs with independent crossings into induced forests. https://arxiv.org/abs/1903.08337

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