@article{22165,
  abstract     = {The book graph 𝐵(𝑘)
𝑛 consists of 𝑛 copies of 𝐾𝑘+1 joined along a common 𝐾𝑘. In the prequel to this paper, we studied the diagonal Ramsey number 𝑟⁡(𝐵(𝑘)
𝑛,𝐵(𝑘)
𝑛). Here we consider the natural off-diagonal variant 𝑟⁡(𝐵(𝑘)
𝑐⁢𝑛,𝐵(𝑘)
𝑛) for fixed 𝑐 ∈(0,1]. In this more general setting, we show that an interesting dichotomy emerges: for very small 𝑐, a simple 𝑘-partite construction dictates the Ramsey function and all nearly-extremal colourings are close to being 𝑘-partite, while, for 𝑐 bounded away from 0, random colourings of an appropriate density are asymptotically optimal and all nearly-extremal colourings are quasirandom. Our investigations also open up a range of questions about what happens for intermediate values of 𝑐.

},
  author       = {Conlon, David and Fox, Jacob and Wigderson, Yuval},
  issn         = {1469-2163},
  journal      = {Combinatorics, Probability and Computing},
  keywords     = {Ramsey theory, book graphs, Ramsey goodness},
  number       = {3},
  pages        = {516--545},
  publisher    = {Cambridge University Press},
  title        = {{Off-diagonal book Ramsey numbers}},
  doi          = {10.1017/s0963548322000360},
  volume       = {32},
  year         = {2023},
}