| 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://dx.doi.org/10.1016/j.jctb.2018.03.001. |
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@article{1688765,
author = {Kráľ, Daniel and Thomas, R and Dvorak, Zdenek},
article_location = {SAN DIEGO},
doi = {http://dx.doi.org/10.1016/j.jctb.2018.03.001},
keywords = {Planar graphs; Girth five; 3-coloring; Critical graphs},
language = {eng},
issn = {0095-8956},
journal = {JOURNAL OF COMBINATORIAL THEORY SERIES B},
title = {Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk},
volume = {132},
year = {2018}
}
TY - JOUR
ID - 1688765
AU - Kráľ, Daniel - Thomas, R - Dvorak, Zdenek
PY - 2018
TI - Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk
JF - JOURNAL OF COMBINATORIAL THEORY SERIES B
VL - 132
SP - 1-46
EP - 1-46
PB - ACADEMIC PRESS INC ELSEVIER SCIENCE
SN - 00958956
KW - Planar graphs
KW - Girth five
KW - 3-coloring
KW - Critical graphs
N2 - 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.
ER -
KRÁĽ, Daniel, R THOMAS and Zdenek DVORAK. Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk. \textit{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://dx.doi.org/10.1016/j.jctb.2018.03.001.
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