---
OA_place: publisher
OA_type: hybrid
_id: '18753'
abstract:
- lang: eng
  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."
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 ."
article_number: '104104'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Alvaro
  full_name: Carbonero, Alvaro
  last_name: Carbonero
- 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
- first_name: Sophie
  full_name: Spirkl, Sophie
  last_name: Spirkl
citation:
  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>
  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>
  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>.
  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.
  ista: Carbonero A, Koerts H, Moore B, Spirkl S. 2025. On heroes in digraphs with
    forbidden induced forests. European Journal of Combinatorics. 125, 104104.
  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>.
  short: A. Carbonero, H. Koerts, B. Moore, S. Spirkl, European Journal of Combinatorics
    125 (2025).
corr_author: '1'
date_created: 2025-01-05T23:01:55Z
date_published: 2025-03-01T00:00:00Z
date_updated: 2025-05-19T14:06:00Z
day: '01'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.1016/j.ejc.2024.104104
external_id:
  arxiv:
  - '2306.04710'
  isi:
  - '001400113700001'
file:
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has_accepted_license: '1'
intvolume: '       125'
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language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: bd95085b-d553-11ed-ba76-e55d3349be45
  grant_number: '101076777'
  name: Randomness and structure in combinatorics
publication: European Journal of Combinatorics
publication_identifier:
  issn:
  - 0195-6698
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: On heroes in digraphs with forbidden induced forests
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 125
year: '2025'
...