3-Coloring Triangle-Free Planar Graphs with a Precolored 9-Cycle

Given a triangle-free planar graph G and a 9-cycle C in G, we characterize situations where a 3-coloring of C does not extend to a proper 3-coloring of G. This extends previous results when C is a cycle of length at most 8. Disciplines Mathematics Comments Choi, Ilkyoo, Jan Ekstein, Přemysl Holub, and Bernard Lidický. "3-coloring triangle-free planar graphs with a precolored 9-cycle." 68 European Journal of Combinatorics (2018): 38-65. doi: 10.1016/j.ejc.2017.07.010. Posted with permission. Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/math_pubs/147 3-coloring triangle-free planar graphs with a precolored 9-cycle Ilkyoo Choi1∗ Jan Ekstein2† Přemysl Holub2‡ Bernard Lidický3§ July 25, 2017 Abstract Given a triangle-free planar graphG and a 9-cycle C inG, we characterize situations where a 3-coloring of C does not extend to a proper 3-coloring of G. This extends previous results when C is a cycle of length at most 8.Given a triangle-free planar graphG and a 9-cycle C inG, we characterize situations where a 3-coloring of C does not extend to a proper 3-coloring of G. This extends previous results when C is a cycle of length at most 8.