Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk

KRÁĽ, Daniel; R THOMAS a Zdenek DVORAK. Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk. JOURNAL OF COMBINATORIAL THEORY SERIES B. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2018, roč. 132, s. 1-46. ISSN 0095-8956. Dostupné z: https://doi.org/10.1016/j.jctb.2018.03.001.

Základní údaje

Originální název

Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk

Autoři

KRÁĽ, Daniel; R THOMAS a Zdenek DVORAK

Vydání

JOURNAL OF COMBINATORIAL THEORY SERIES B, SAN DIEGO, ACADEMIC PRESS INC ELSEVIER SCIENCE, 2018, 0095-8956

---

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.892

DOI

https://doi.org/10.1016/j.jctb.2018.03.001

UT WoS

000439085700001

Klíčová slova anglicky

Planar graphs; Girth five; 3-coloring; Critical graphs

---

Anotace

V originále

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.