{"file_date_updated":"2025-03-20T09:46:20Z","doi":"10.1112/jlms.70116","article_number":"e70116","publication_status":"published","volume":111,"publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publisher":"Wiley","oa":1,"author":[{"full_name":"Draganić, Nemanja","first_name":"Nemanja","last_name":"Draganić"},{"first_name":"Kalina H","full_name":"Petrova, Kalina H","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","last_name":"Petrova"}],"external_id":{"arxiv":["2207.05048"]},"abstract":[{"lang":"eng","text":"The size-Ramsey number r^(H) of a graph H is the smallest number of edges a (host) graph G can have, such that for any red/blue colouring of G, there is a monochromatic copy of H in G. Recently, Conlon, Nenadov and Trujić showed that if H is a graph on n vertices and maximum degree three, then r^(H)=O(n8/5), improving upon the upper bound of n5/3+o(1) by Kohayakawa, Rödl, Schacht and Szemerédi. In this paper we show that r^(H)≤n3/2+o(1). While the previously used host graphs were vanilla binomial random graphs, we prove our result using a novel host graph construction. Our bound hits a natural barrier of the existing methods."}],"file":[{"file_id":"19427","date_created":"2025-03-20T09:46:20Z","date_updated":"2025-03-20T09:46:20Z","content_type":"application/pdf","creator":"dernst","success":1,"access_level":"open_access","file_name":"2025_JournLondonMath_Draganic.pdf","relation":"main_file","checksum":"d8e0a03286a44c4f672709e3c829206e","file_size":625974}],"scopus_import":"1","article_processing_charge":"No","OA_type":"hybrid","publication":"Journal of the London Mathematical Society","year":"2025","language":[{"iso":"eng"}],"acknowledgement":"We would like to thank Rajko Nenadov and Miloš Trujić for helpful comments and discussions, as well as the anonymous referees for their very useful feedback, which improved the paper considerably. This research was supported by SNSF Project 217926. Part of this research was conducted while Nemanja Draganić was at ETH Zürich, Switzerland, and partially supported by SNSF Grant 200021_196965. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement Number: 101034413. Part of this research was conducted while Kalina Petrova was at the Department of Computer Science, ETH Zürich, Switzerland, supported by SNSF Grant CRSII5 173721.","day":"01","title":"Size‐Ramsey numbers of graphs with maximum degree three","date_updated":"2025-03-20T09:47:50Z","license":"https://creativecommons.org/licenses/by/4.0/","department":[{"_id":"MaKw"}],"month":"03","type":"journal_article","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","quality_controlled":"1","project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"date_published":"2025-03-01T00:00:00Z","OA_place":"publisher","arxiv":1,"issue":"3","intvolume":"       111","_id":"19418","oa_version":"Published Version","article_type":"original","has_accepted_license":"1","date_created":"2025-03-19T09:03:37Z","ec_funded":1,"citation":{"chicago":"Draganić, Nemanja, and Kalina H Petrova. “Size‐Ramsey Numbers of Graphs with Maximum Degree Three.” <i>Journal of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/jlms.70116\">https://doi.org/10.1112/jlms.70116</a>.","mla":"Draganić, Nemanja, and Kalina H. Petrova. “Size‐Ramsey Numbers of Graphs with Maximum Degree Three.” <i>Journal of the London Mathematical Society</i>, vol. 111, no. 3, e70116, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/jlms.70116\">10.1112/jlms.70116</a>.","ama":"Draganić N, Petrova KH. Size‐Ramsey numbers of graphs with maximum degree three. <i>Journal of the London Mathematical Society</i>. 2025;111(3). doi:<a href=\"https://doi.org/10.1112/jlms.70116\">10.1112/jlms.70116</a>","ieee":"N. Draganić and K. H. Petrova, “Size‐Ramsey numbers of graphs with maximum degree three,” <i>Journal of the London Mathematical Society</i>, vol. 111, no. 3. Wiley, 2025.","ista":"Draganić N, Petrova KH. 2025. Size‐Ramsey numbers of graphs with maximum degree three. Journal of the London Mathematical Society. 111(3), e70116.","apa":"Draganić, N., &#38; Petrova, K. H. (2025). Size‐Ramsey numbers of graphs with maximum degree three. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.70116\">https://doi.org/10.1112/jlms.70116</a>","short":"N. Draganić, K.H. Petrova, Journal of the London Mathematical Society 111 (2025)."}}