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PreprintCC BY 4.0arXiv

Non-isomorphic graphs have distinct vertex-Ramsey classes

  • Maria Axenovich
  • Patrick Schmitteckert
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Abstract

For a graph H, its k-colour vertex Ramsey class is the set of all graphs G such that any colouring of the vertices of G in k colours results in a monochromatic (induced) copy of H. We prove that for any k, Ramsey classes of any non-isomorphic graphs are distinct.

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Cite

BibTeXRIS
BibTeX
@misc{axenovich2026nonisomorphic,
  title = {{Non-isomorphic graphs have distinct vertex-Ramsey classes}},
  author = {Maria Axenovich and Patrick Schmitteckert},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03704},
  eprint = {2610.03704},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03704},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-isomorphic graphs have distinct vertex-Ramsey classes
AU  - Maria Axenovich
AU  - Patrick Schmitteckert
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03704
UR  - https://arxiv.org/abs/2610.03704
AB  - For a graph H, its k-colour vertex Ramsey class is the set of all graphs G such that any colouring of the vertices of G in k colours results in a monochromatic (induced) copy of H. We prove that for any k, Ramsey classes of any non-isomorphic graphs are distinct.
ER  -