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

KRÁĽ, Daniel; R THOMAS and 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, vol. 132, p. 1-46. ISSN 0095-8956. Available from: https://doi.org/10.1016/j.jctb.2018.03.001.

Basic information

Original name

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

Authors

KRÁĽ, Daniel; R THOMAS and Zdenek DVORAK

Edition

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

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Other information

Language

English

Type of outcome

Article in a journal

Confidentiality degree

is not subject to a state or trade secret

Impact factor

Impact factor: 0.892

DOI

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

UT WoS

000439085700001

Keywords in English

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

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Abstract

In the original language

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.