Covering projective planar graphs with three forests (Q2075505)

A graph \(G\) is said to be \(F(d_1, d_2,\dots,d_k)\)-coverable if \(G\) can be covered by \(k\) forests \(F_1,F_2,\dots,F_k\) such that the maximum degree \(\Delta(F_i)\) is at most \(d_i\) for each \(i=1,2,\dots,k\). If \(d_i=\infty\), then the maximum degree of \(F_i\) is unbounded. \textit{D. Gonçalves} [J. Comb. Theory, Ser. B 99, No. 2, 314--322 (2009; Zbl 1205.05179)] verified that every planar graph is \(F(\infty,\infty,4)\)-coverable. In this paper, the authors prove a similar result for a projective planar graph, that is, they claim that every projective planar graph is \(F(\infty,\infty,4)\)-coverable. Furthermore, they use a new technique to verify the main result.