Publication details
Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes of 4-critical graphs
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Combinatorial Theory. Series B |
| MU Faculty or unit | |
| Citation | |
| Web | http://dx.doi.org/10.1016/j.jctb.2020.09.001 |
| Doi | http://dx.doi.org/10.1016/j.jctb.2020.09.001 |
| Keywords | Graph coloring; Graphs on surfaces; Triangle-free |
| Description | Let G be a 4-critical graph with t triangles, embedded in a surface of genus g. Let c be the number of 4-cycles in G that do not bound a 2-cell face. We prove that 1] f face of G (|f| & minus; 4) <= kappa(g +t + c & minus; 1) for a fixed constant kappa, thus generalizing and strengthening several known results. As a corollary, we prove that every triangle-free graph G embedded in a surface of genus g contains a set of O(g) vertices such that G & minus; X is 3-colorable. (c) 2020 Elsevier Inc. All rights reserved. |