Informace o publikaci
Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes of 4-critical graphs
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| Rok publikování | 2021 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Journal of Combinatorial Theory. Series B |
| Fakulta / Pracoviště MU | |
| Citace | DVOŘÁK, Zdeněk, Daniel KRÁĽ a Robin THOMAS. Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes of 4-critical graphs. Journal of Combinatorial Theory. Series B. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2021, roč. 150, September 2021, s. 270-304. ISSN 0095-8956. Dostupné z: https://dx.doi.org/10.1016/j.jctb.2020.09.001. |
| www | http://dx.doi.org/10.1016/j.jctb.2020.09.001 |
| Doi | http://dx.doi.org/10.1016/j.jctb.2020.09.001 |
| Klíčová slova | Graph coloring; Graphs on surfaces; Triangle-free |
| Popis | 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. |