@article{1a781be704064b56ab0ba3145e0fc291,
title = "A survey of χ-boundedness",
abstract = "If a graph has bounded clique number and sufficiently large chromatic number, what can we say about its induced subgraphs? Andr{\'a}s Gy{\'a}rf{\'a}s made a number of challenging conjectures about this in the early 1980s, which have remained open until recently; but in the last few years there has been substantial progress. This is a survey of where we are now.",
keywords = "colouring, χ-boundedness",
author = "Alex Scott and Paul Seymour",
note = "Funding Information: Several people have sent us corrections or improvements. We would particularly like to thank Pierre Aboulker, Pierre Charbit, Louis Esperet, Patrice Ossona de Mendez, Sang-Il Oum, Bruce Reed, Vaidy Sivaraman, Sophie Spirkl, and Nicolas Trotignon. Also, we would like to thank the referees for an exceptionally helpful set of comments. Alex Scott was supported by a Leverhulme Trust Research Fellowship. Paul Seymour was supported by ONR grant N00014-14-1-0084, NSF grants DMS-1265563 and DMS-1800053 and AFOSR grant 9550-19-1-0187. Funding Information: Alex Scott was supported by a Leverhulme Trust Research Fellowship. Paul Seymour was supported by ONR grant N00014‐14‐1‐0084, NSF grants DMS‐1265563 and DMS‐1800053 and AFOSR grant 9550‐19‐1‐0187. Publisher Copyright: {\textcopyright} 2020 Wiley Periodicals LLC",
year = "2020",
month = nov,
day = "1",
doi = "10.1002/jgt.22601",
language = "English (US)",
volume = "95",
pages = "473--504",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "3",
}