Paper Contents
Abstract
In a graph , a list assignment is a function that it assigns a list of colors to each vertex An coloring is a mapping that assigns a color to each vertex so that at most impropriety neighbors of are the same color with . A graph is said to be choosable if it admits an coloring for every list assignment with for all . In this paper, we prove that every planar graph with neither adjacent triangles nor 7-cycles is choosable. In 2016, Min Chen, Andre Raspaud and Weifan Wang proved that every planar graph with neither adjacent triangles nor 6-cycles is choosable.Keywords: Planar graphs, improper choosability, cycle.
Copyright
Copyright © 2024 Oothan Nweit. This is an open access article distributed under the Creative Commons Attribution License.
