@article{19418,
  abstract     = {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.},
  author       = {Draganić, Nemanja and Petrova, Kalina H},
  issn         = {1469-7750},
  journal      = {Journal of the London Mathematical Society},
  number       = {3},
  publisher    = {Wiley},
  title        = {{Size‐Ramsey numbers of graphs with maximum degree three}},
  doi          = {10.1112/jlms.70116},
  volume       = {111},
  year         = {2025},
}