Choosability and edge choosability of planar graphs without five cycles
It is proved that every planar graph \(G\) of minimum degree \(\geq 3\) without cycles of length 5 contains an edge \(xy\) with degree-3 vertex \(x\) and degree-\((\leq 5)\) vertex \(y\). Based on this result the authors prove that \(G\) is four choosable and also edge-\((\delta(G)+1)\)-choosable.
scientific article; zbMATH DE number 1781919