DP-colouring Of Planar Graphs

This thesis studies DP-colouring,fractional DP-colouring and defective DP-colouring of planar graphs.In 2017,Dvo(?)k and Postle introduced DP-colouring as a generalization of list colouring.This paper proves that every triangle-free planar graph in which 4-cycle do not share edges with other 4-or 5-cycles is DP-3-colourable.This implies that every triangle-free planar graph without 6-or 7-cycles is DP-3-colourable.The concept of fractional DP-colouring of a graph was introduced by Bernshteyn,Kostochka and Zhu.Here we consider planar graphs of large girth and prove the following theorem:For any integer k≥1,every planar graph G of girth at least 8k-3 has fractional DP-chromatic number at most 2+1/k.For defective DP-coloring of planar graphs,we prove every planar graphs without 4-cycles and l-cycles for some l ∈ {5,6,7,8,9} is 1-defective DP-3-colourable.