The k-color poset Ramsey number of the diamond is 2k

@misc{bohman2026kcolor,
  title = {{The $k$-color poset Ramsey number of the diamond is $2k$}},
  author = {Tom Bohman and Will Cong and Quentin Dubroff and Teresa Huang and Zheyuan Li and BangTam Ngo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20545},
  eprint = {2610.20545},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20545},
  note = {CC BY-NC-ND 4.0},
}

TY  - UNPB
TI  - The k-color poset Ramsey number of the diamond is 2k
AU  - Tom Bohman
AU  - Will Cong
AU  - Quentin Dubroff
AU  - Teresa Huang
AU  - Zheyuan Li
AU  - BangTam Ngo
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20545
UR  - https://arxiv.org/abs/2610.20545
AB  - The k-color Ramsey number of a poset P is the smallest dimension d such that any k-coloring of the d-dimensional Boolean lattice contains a monochromatic induced copy of P. For $ j\ge 2$ the j-diamond is the poset that consists of a maximum element, a minimum element and an antichain of size j. We prove that the k-color Ramsey number of the j-diamond is at most jk. Colorings of the Boolean lattice that assign sets of the same size the same color provide matching lower bounds for j ∈ {2,3,4}.
ER  -