Wu, Zhang, and Li's equitable induced-forest partition conjecture for planar graphs

Let GG be a planar graph. An equitable partition of GG is a partition of its vertex set into parts whose sizes differ by at most one, and an induced forest is a vertex-induced subgraph that is a forest. Wu, Zhang, and Li's conjecture. There is a constant cc such that, for every integer kck\geqslant c, every planar graph can be equitably partitioned into kk induced forests. The conjecture concerns equitable coloring by induced forests; the cited paper proves that such a constant exists, so the claim is resolved.

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Primary source

Louis Esperet, Laetitia Lemoine and Frédéric Maffray, “Equitable partition of graphs into induced forests”, arXiv:1410.0861 (2015).

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