@article{10b11b9e2a494e348c847acd7d368517,
title = "Proof of a conjecture of Plummer and Zha",
abstract = "Say a graph (Formula presented.) is a pentagraph if every cycle has length at least five, and every induced cycle of odd length has length five. Robertson proposed the conjecture that the Petersen graph is the only internally 4-connected pentagraph, but this was disproved by Plummer and Zha in 2014. Plummer and Zha conjectured that every internally 4-connected pentagraph is three-colourable. We prove this: indeed, we will prove that every pentagraph is three-colourable.",
keywords = "colouring, induced subgraph, pentagraph",
author = "Maria Chudnovsky and Paul Seymour",
note = "Funding Information: This research was conducted during an Oberwolfach workshop on graph theory in January 2022, and the authors are grateful to MFO for providing accommodations and facilities. We would like to thank Xingxing Yu for introducing us to this problem (at an open problem session during the workshop) and for supplying background information. This study was supported by NSF DMS‐EPSRC grant DMS‐2120644 (Maria Chudnovsky) and AFOSR grant A9550‐19‐1‐0187 (Paul Seymour). Funding Information: This research was conducted during an Oberwolfach workshop on graph theory in January 2022, and the authors are grateful to MFO for providing accommodations and facilities. We would like to thank Xingxing Yu for introducing us to this problem (at an open problem session during the workshop) and for supplying background information. This study was supported by NSF DMS-EPSRC grant DMS-2120644 (Maria Chudnovsky) and AFOSR grant A9550-19-1-0187 (Paul Seymour). Publisher Copyright: {\textcopyright} 2023 Wiley Periodicals LLC.",
year = "2023",
doi = "10.1002/jgt.22926",
language = "English (US)",
volume = "103",
pages = "437--450",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "3",
}