A note on 3-choosability of plane graphs under distance restrictions
Jing Jin, Yiming Wei · Discrete Mathematics Algorithms and Applications · 2016
A graph [Formula: see text] is [Formula: see text]-choosable if it has an [Formula: see text]-coloring whenever [Formula: see text] is a list assignment such that [Formula: see text] for all [Formula: see text]. We provide two sufficient conditions for 3-choosability of plane graphs. Every plane graph with [Formula: see text] without cycles of length from 4 to 6 and special 7-cycles is 3-choosable. Every plane graph with [Formula: see text] without cycles of length from 4 to 5 and adjacent 6-cycles is also 3-choosable.