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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