---
res:
  bibo_abstract:
  - "A highly influential result of Nikiforov states that if an n-vertex graph G contains\r\nat
    least γnh copies of a fixed h-vertex graph H, then G contains a blowup of H of
    order\r\nΩγ,H(logn). While the dependence on n is optimal, the correct dependence
    on γ is unknown;\r\nall known proofs yield bounds that are polynomial in γ, but
    the best known upper bound,\r\ncoming from random graphs, is only logarithmic
    in γ. It is a major open problem to narrow\r\nthis gap.\r\nWe prove that if H
    is triangle-free, then the logarithmic behavior of the upper bound\r\nis the truth.
    That is, under the assumptions above, G contains a blowup of H of order\r\nΩH(logn/log(1/γ)).
    This is the first non-trivial instance where the optimal dependence in\r\nNikiforov’s
    theorem is known.\r\nAs a consequence, we also prove an upper bound on multicolor
    Ramsey numbers of\r\nblowups of triangle-free graphs, proving that the dependence
    on the number of colors is\r\npolynomial once the blowup is sufficiently large.
    This shows that, from the perspective\r\nof multicolor Ramsey numbers, blowups
    of fixed triangle-free graphs behave like bipartite\r\ngraphs.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: António
      foaf_name: Girão, António
      foaf_surname: Girão
  - foaf_Person:
      foaf_givenName: Zach
      foaf_name: Hunter, Zach
      foaf_surname: Hunter
  - foaf_Person:
      foaf_givenName: Yuval
      foaf_name: Wigderson, Yuval
      foaf_surname: Wigderson
      foaf_workInfoHomepage: http://www.librecat.org/personId=2d0023a0-1567-11f0-833d-d5c1e476d4b5
  bibo_doi: 10.19086/aic.2025.10
  bibo_volume: 10
  dct_date: 2025^xs_gYear
  dct_language: eng
  dct_publisher: Alliance of Diamond Open Access Journals@
  dct_title: Blowups of triangle-free graphs@
...