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arXiv · 2007.01517

Decomposing planar graphs into graphs with degree restrictions

Eun-Kyung Cho·Ilkyoo Choi·Ringi Kim·Boram Park·Tingting Shan·Xuding Zhu
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Abstract

Given a graph $G$, a decomposition of $G$ is a partition of its edges. A graph is $(d, h)$-decomposable if its edge set can be partitioned into a $d$-degenerate graph and a graph with maximum degree at most $h$. For $d \le 4$, we are interested in the minimum integer $h_d$ such that every planar graph is $(d,h_d)$-decomposable. It was known that $h_3 \le 4$, $h_2\le 8$, and $h_1 = \infty$. This paper proves that $h_4=1, h_3=2$, and $4 \le h_2 \le 6$.

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Eun-Kyung Cho, Ilkyoo Choi, Ringi Kim, Boram Park, Tingting Shan, Xuding Zhu. 2020-07-03. Decomposing planar graphs into graphs with degree restrictions. https://arxiv.org/abs/2007.01517

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