Publication details
Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | JOURNAL OF COMBINATORIAL THEORY SERIES B |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.jctb.2018.03.001 |
| Keywords | Planar graphs; Girth five; 3-coloring; Critical graphs |
| Description | Let G be a plane graph of girth at least five. We show that if there exists a 3-coloring Phi of a cycle C of G that does not extend to a 3-coloring of G, then G has a subgraph H on O(|C|) vertices that also has no 3-coloring extending Phi. This is asymptotically best possible and improves a previous bound of Thomassen. In the next paper of the series we will use this result and the attendant theory to prove a generalization to graphs on surfaces with several precolored cycles. (C) 2018 Elsevier Inc. All rights reserved. |