Akiyama–Watanabe and Albertson–Rhaas conjecture for bipartite planar graphs

Let GG be a bipartite planar graph of order nn. An induced forest of GG is a vertex-induced subgraph that is acyclic. Akiyama–Watanabe and Albertson–Rhaas conjecture. Every bipartite planar graph of order nn admits an induced forest of order at least 5n8\frac{5n}{8}. This conjecture strengthens the general planar-graph bound for the bipartite subclass; the paper records it as an independently proposed open question.

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Primary source

François Dross, Mickael Montassier and Alexandre Pinlou, “Large induced forests in planar graphs with girth 4 or 5”, arXiv:1409.1348 (2014).

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