@article{13e8f75797334320aa0ee199aa8d7720,
title = "Coloring graphs with no induced five-vertex path or gem",
abstract = "For a graph (Formula presented.), let (Formula presented.) and (Formula presented.), respectively, denote the chromatic number and clique number of (Formula presented.). We give an explicit structural description of ((Formula presented.), gem)-free graphs, and show that every such graph (Formula presented.) satisfies (Formula presented.). Moreover, this bound is best possible. Here a gem is the graph that consists of an induced four-vertex path plus a vertex which is adjacent to all the vertices of that path.",
keywords = "P-free graphs, chromatic number, clique number, χ-boundedness",
author = "Maria Chudnovsky and T. Karthick and Peter Maceli and Fr{\'e}d{\'e}ric Maffray",
note = "Funding Information: The authors would like to dedicate this paper to the memory of Professor Frederic Maffray (deceased on August 22, 2018). The authors thank the referees for their suggestions and comments. The first author is supported by the NSF grant DMS-1763817, and supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under grant number W911NF-16-1-0404. The second author would like to thank Mathew C. Francis for helpful discussions, and his research is partially supported by DST-SERB, Government of India under MATRICS scheme. Funding Information: The authors would like to dedicate this paper to the memory of Professor Frederic Maffray (deceased on August 22, 2018). The authors thank the referees for their suggestions and comments. The first author is supported by the NSF grant DMS‐1763817, and supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under grant number W911NF‐16‐1‐0404. The second author would like to thank Mathew C. Francis for helpful discussions, and his research is partially supported by DST‐SERB, Government of India under MATRICS scheme. Publisher Copyright: {\textcopyright} 2020 Wiley Periodicals, Inc.",
year = "2020",
month = dec,
day = "1",
doi = "10.1002/jgt.22572",
language = "English (US)",
volume = "95",
pages = "527--542",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "4",
}