Akiyama–Watanabe–Albertson–Haas conjecture on induced forests in bipartite planar graphs

Let GG be a finite simple bipartite planar graph of order nn. An induced forest is a vertex-induced subgraph of GG that is a forest.

Akiyama–Watanabe–Albertson–Haas conjecture. Every bipartite planar graph of order nn admits an induced forest of order at least

5n8.\frac{5n}{8}.

This strengthens the general lower-bound problem for planar graphs by imposing bipartiteness and seeking a larger induced forest. The source states the conjecture but gives no resolution; partial lower bounds and related results are discussed.

Sources & referencesView supporting material

Primary source

François Dross, Mickael Montassier and Alexandre Pinlou, “A lower bound on the order of the largest induced forest in planar graphs with high girth”, arXiv:1504.01949 (2015).

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