PreprintCC BY 4.0arXiv
Decay-Ramsey Sequences
Abstract
Given a sequence a=(ai)i≥ 1 of positive real numbers, we say that a colouring c:E(Kn)→ ℕ is a-bounded if the proportion of edges coloured i is at most ai, for all i. We write a → Kk if, for all sufficiently large n, all a-bounded colourings c:E(Kn)→ ℕ contain a monochromatic Kk. We say that the sequence a is \emph{Decay-Ramsey} if a→ Kk for all k≥ 2. In this short paper we introduce the question of determining which sequences are Decay-Ramsey and present some initial results.
Related
BibTeX
@misc{braccio2026decayramsey,
title = {{Decay-Ramsey Sequences}},
author = {Francesco Di Braccio and Simon Griffiths and Pedram Noohi and Leo Versteegen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20577},
eprint = {2610.20577},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20577},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Decay-Ramsey Sequences
AU - Francesco Di Braccio
AU - Simon Griffiths
AU - Pedram Noohi
AU - Leo Versteegen
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20577
UR - https://arxiv.org/abs/2610.20577
AB - Given a sequence a=(a_i)_i≥ 1 of positive real numbers, we say that a colouring c:E(K_n)→ ℕ is a-bounded if the proportion of edges coloured i is at most a_i, for all i. We write a → K_k if, for all sufficiently large n, all a-bounded colourings c:E(K_n)→ ℕ contain a monochromatic K_k. We say that the sequence a is \emph{Decay-Ramsey} if a→ K_k for all k≥ 2. In this short paper we introduce the question of determining which sequences are Decay-Ramsey and present some initial results.
ER -