Defective DP-coloring Of Planar Graphs

This paper proves that every planar graph G contains a subgraph H with ?(H)?6 such that G-E(H)is 2-degenerate.As a consequence of this result,every planar graph G is 6-defective DP 3-colorable.On the other hand,we show that there is a planar graph which is not 3-defective DP 3-colourable.It remains an open problem whether every planar graph is d-defective DP 3-colourable,for d=4,5.