{"OA_type":"hybrid","oa_version":"Published Version","day":"01","isi":1,"quality_controlled":"1","date_updated":"2025-05-19T14:06:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"arxiv":1,"publication_status":"published","month":"03","publication_identifier":{"issn":["0195-6698"]},"volume":125,"year":"2025","article_processing_charge":"Yes (in subscription journal)","citation":{"short":"A. Carbonero, H. Koerts, B. Moore, S. Spirkl, European Journal of Combinatorics 125 (2025).","chicago":"Carbonero, Alvaro, Hidde Koerts, Benjamin Moore, and Sophie Spirkl. “On Heroes in Digraphs with Forbidden Induced Forests.” <i>European Journal of Combinatorics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ejc.2024.104104\">https://doi.org/10.1016/j.ejc.2024.104104</a>.","ama":"Carbonero A, Koerts H, Moore B, Spirkl S. On heroes in digraphs with forbidden induced forests. <i>European Journal of Combinatorics</i>. 2025;125. doi:<a href=\"https://doi.org/10.1016/j.ejc.2024.104104\">10.1016/j.ejc.2024.104104</a>","mla":"Carbonero, Alvaro, et al. “On Heroes in Digraphs with Forbidden Induced Forests.” <i>European Journal of Combinatorics</i>, vol. 125, 104104, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ejc.2024.104104\">10.1016/j.ejc.2024.104104</a>.","apa":"Carbonero, A., Koerts, H., Moore, B., &#38; Spirkl, S. (2025). On heroes in digraphs with forbidden induced forests. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2024.104104\">https://doi.org/10.1016/j.ejc.2024.104104</a>","ista":"Carbonero A, Koerts H, Moore B, Spirkl S. 2025. On heroes in digraphs with forbidden induced forests. European Journal of Combinatorics. 125, 104104.","ieee":"A. Carbonero, H. Koerts, B. Moore, and S. Spirkl, “On heroes in digraphs with forbidden induced forests,” <i>European Journal of Combinatorics</i>, vol. 125. Elsevier, 2025."},"type":"journal_article","acknowledgement":"We thank the anonymous referees for their careful proofreading which helped improve the presentation of this paper. We also thank one of the anonymous referees for pointing out our construction implies Theorem 1.7!\r\nBenjamin Moore finished this project while a postdoctoral researcher at Charles University, and was supported by project 22-17398S (Flows and cycles in graphs on surfaces) of the Czech Science Foundation. Benjamin Moore is currently funded by RANDSTRUCT No. 101076777, and appreciates the gracious support. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number RGPIN-2020-03912]. Cette recherche a été financée par le Conseil de recherches en sciences naturelles et en génie du Canada (CRSNG), [numéro de référence RGPIN-2020-03912]. This project was funded in part by the Government of Ontario .","tmp":{"image":"/images/cc_by.png","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)"},"date_published":"2025-03-01T00:00:00Z","OA_place":"publisher","has_accepted_license":"1","department":[{"_id":"MaKw"}],"abstract":[{"text":"We continue a line of research which studies which hereditary families of digraphs have bounded dichromatic number. For a class of digraphs  C, a hero in  C  is any digraph  H\r\n  such that  H -free digraphs in  C  have bounded dichromatic number. We show that if  F\r\n  is an oriented star of degree at least five, the only heroes for the class of  F -free digraphs are transitive tournaments. For oriented stars  F  of degree exactly four, we show the only heroes in  F -free digraphs are transitive tournaments, or possibly special joins of transitive tournaments. Aboulker et al. characterized the set of heroes of  {H,K1+P2→} -free digraphs almost completely, and we show the same characterization for the class of  {H,rK1+P3→} -free digraphs. Lastly, we show that if we forbid two \"valid\" orientations of brooms, then every transitive tournament is a hero for this class of digraphs.","lang":"eng"}],"language":[{"iso":"eng"}],"ddc":["510"],"doi":"10.1016/j.ejc.2024.104104","external_id":{"arxiv":["2306.04710"],"isi":["001400113700001"]},"project":[{"name":"Randomness and structure in combinatorics","grant_number":"101076777","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"corr_author":"1","file_date_updated":"2025-04-16T09:16:25Z","publisher":"Elsevier","article_number":"104104","article_type":"original","intvolume":"       125","status":"public","title":"On heroes in digraphs with forbidden induced forests","date_created":"2025-01-05T23:01:55Z","author":[{"last_name":"Carbonero","full_name":"Carbonero, Alvaro","first_name":"Alvaro"},{"first_name":"Hidde","full_name":"Koerts, Hidde","last_name":"Koerts"},{"first_name":"Benjamin","full_name":"Moore, Benjamin","id":"6dc1a1be-bf1c-11ed-8d2b-d044840f49d6","last_name":"Moore"},{"last_name":"Spirkl","first_name":"Sophie","full_name":"Spirkl, Sophie"}],"publication":"European Journal of Combinatorics","_id":"18753","scopus_import":"1","file":[{"date_updated":"2025-04-16T09:16:25Z","checksum":"2c75f78f40ebb93d16fe3765bda2905a","creator":"dernst","success":1,"file_id":"19577","file_name":"2025_EuropJournCombinatorics_Carbonero.pdf","date_created":"2025-04-16T09:16:25Z","access_level":"open_access","relation":"main_file","file_size":1110657,"content_type":"application/pdf"}]}