{"language":[{"iso":"eng"}],"acknowledgement":"This work was initiated at the annual workshop of the Combinatorics and Graph Theory group of Freie Universität Berlin in Wilhelmsaue in September 2023. The authors would like to thank the institution for enabling this research. Finally, the fourth author would like to thank Tibor Szabó and the Combinatorics and Graph Theory group at Freie Universität Berlin for their hospitality during the research visit. Additionally, we thank Moharram Iradmusa for bringing the papers [5], [7] to our attention. Finally, we thank the anonymous referees for their suggestions on the manuscript, which have improved the quality of the document.\r\nM.A.: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413 .\r\nS.B.: The research leading to these results was supported by EPSRC, UK, grant no. EP/V048287/1. There are no additional data beyond that contained within the main manuscript.\r\nS.R.: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689).\r\nJ.R. acknowledges the support of the Grant PID2020-113082GB-I00 funded by MICIU/AEI/10.13039/501100011033, Spain, and the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D, Spain (CEX2020-001084-M).","intvolume":"       360","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","publisher":"Elsevier","oa_version":"Published Version","_id":"18478","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.dam.2024.10.002"}],"arxiv":1,"publication_status":"epub_ahead","author":[{"full_name":"Anastos, Michael","last_name":"Anastos","first_name":"Michael","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb"},{"full_name":"Boyadzhiyska, Simona","last_name":"Boyadzhiyska","first_name":"Simona"},{"full_name":"Rathke, Silas","last_name":"Rathke","first_name":"Silas"},{"first_name":"Juanjo","full_name":"Rué, Juanjo","last_name":"Rué"}],"title":"On the chromatic number of powers of subdivisions of graphs","abstract":[{"lang":"eng","text":"For a given graph G=(V,E), we define its \\emph{nth subdivision} as the graph obtained from G by replacing every edge by a path of length n. We also define the \\emph{mth power} of G as the graph on vertex set V where we connect every pair of vertices at distance at most m in G. In this paper, we study the chromatic number of powers of subdivisions of graphs and resolve the case m=n asymptotically. In particular, our result confirms a conjecture of Mozafari-Nia and Iradmusa in the case m=n=3 in a strong sense."}],"oa":1,"date_created":"2024-10-27T23:01:44Z","page":"506-511","quality_controlled":"1","corr_author":"1","day":"23","doi":"10.1016/j.dam.2024.10.002","article_type":"original","external_id":{"arxiv":["2404.05542"]},"publication":"Discrete Applied Mathematics","year":"2024","date_updated":"2024-11-04T10:05:41Z","scopus_import":"1","ec_funded":1,"month":"10","publication_identifier":{"issn":["0166-218X"]},"project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"citation":{"apa":"Anastos, M., Boyadzhiyska, S., Rathke, S., &#38; Rué, J. (2024). On the chromatic number of powers of subdivisions of graphs. <i>Discrete Applied Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.dam.2024.10.002\">https://doi.org/10.1016/j.dam.2024.10.002</a>","ista":"Anastos M, Boyadzhiyska S, Rathke S, Rué J. 2024. On the chromatic number of powers of subdivisions of graphs. Discrete Applied Mathematics. 360, 506–511.","short":"M. Anastos, S. Boyadzhiyska, S. Rathke, J. Rué, Discrete Applied Mathematics 360 (2024) 506–511.","chicago":"Anastos, Michael, Simona Boyadzhiyska, Silas Rathke, and Juanjo Rué. “On the Chromatic Number of Powers of Subdivisions of Graphs.” <i>Discrete Applied Mathematics</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.dam.2024.10.002\">https://doi.org/10.1016/j.dam.2024.10.002</a>.","mla":"Anastos, Michael, et al. “On the Chromatic Number of Powers of Subdivisions of Graphs.” <i>Discrete Applied Mathematics</i>, vol. 360, Elsevier, 2024, pp. 506–11, doi:<a href=\"https://doi.org/10.1016/j.dam.2024.10.002\">10.1016/j.dam.2024.10.002</a>.","ieee":"M. Anastos, S. Boyadzhiyska, S. Rathke, and J. Rué, “On the chromatic number of powers of subdivisions of graphs,” <i>Discrete Applied Mathematics</i>, vol. 360. Elsevier, pp. 506–511, 2024.","ama":"Anastos M, Boyadzhiyska S, Rathke S, Rué J. On the chromatic number of powers of subdivisions of graphs. <i>Discrete Applied Mathematics</i>. 2024;360:506-511. doi:<a href=\"https://doi.org/10.1016/j.dam.2024.10.002\">10.1016/j.dam.2024.10.002</a>"},"OA_place":"publisher","article_processing_charge":"Yes (in subscription journal)","date_published":"2024-10-23T00:00:00Z","department":[{"_id":"MaKw"}],"volume":360,"OA_type":"hybrid","status":"public"}