@article{a265b666b4904240b8aedfde67f1241a,
title = "Triangle-free graphs that do not contain an induced subdivision of K4 are 3-colorable",
abstract = "We show that triangle-free graphs that do not contain an induced subgraph isomorphic to a subdivision of K4 are 3-colorable. This proves a conjecture of Trotignon and Vu{\v s}kovi{\'c} [J. Graph Theory. 84 (2017), no. 3, pp. 233–248].",
keywords = "coloring, induced subgraph",
author = "Maria Chudnovsky and Chun-Hung Liu and Oliver Schaudt and Sophie Spirkl and Nicolas Trotignon and Kristina Vu{\v s}kovi{\'c}",
note = "Funding Information: We are thankful to Paul Seymour and Mingxian Zhong for many helpful discussions. This material is based upon work supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office (under grant number W911NF-16-1-0404). Maria Chudnovsky was supported by NSF grant (DMS-1550991) and U.S. Army Research Office grant (W911NF-16-1-0404). Chun-Hung Liu was supported by NSF grant (DMS-1664593). Nicolas Trotignon was partially supported by ANR project Stint (under reference ANR-13-BS02-0007) and by the LABEX MILYON (ANR-10-LABX-0070) of Universit{\'e} de Lyon, within the program “Investissements d{\textquoteright}Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). Kristina Vu{\v s}kovi{\'c} was partially supported by EPSRC grant (EP/N0196660/1), and Serbian Ministry of Education, Science and Technological Development (174033 and III44006). Publisher Copyright: {\textcopyright} 2018 Wiley Periodicals, Inc.",
year = "2019",
month = oct,
doi = "10.1002/jgt.22441",
language = "English (US)",
volume = "92",
pages = "67--95",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "2",
}