3‐Coloring Triangle‐Free Planar Graphs with a Precolored 8‐Cycle
Zdenĕk Dvořák, Bernard Lidický · Journal of Graph Theory · 2014
Abstract Let G be a planar triangle‐free graph and let C be a cycle in G of length at most 8. We characterize all situations where a 3‐coloring of C does not extend to a proper 3‐coloring of the whole graph.