PreprintCC BY 4.0arXiv
New results on cyclic and ordered Ramsey numbers
Abstract
Inspired by the work of Poljak, Bašić, Damnjanović, Stevanović, and Stošić used the Kissat SAT solver in a recent paper to systematically determine the small cyclic and ordered Ramsey numbers of several families of graphs. By studying the patterns in their data, Bašić et al. formulated 15 conjectures on cyclic and ordered Ramsey numbers. In this paper, we confirm 9 of their conjectures, trace confirmations of 2 more to existing literature, and, perhaps surprisingly, disprove another one.
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BibTeX
@misc{kucheriya2026results,
title = {{New results on cyclic and ordered Ramsey numbers}},
author = {Gaurav Kucheriya and Jan Petr and Jun Yan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08375},
eprint = {2611.08375},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08375},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New results on cyclic and ordered Ramsey numbers
AU - Gaurav Kucheriya
AU - Jan Petr
AU - Jun Yan
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08375
UR - https://arxiv.org/abs/2611.08375
AB - Inspired by the work of Poljak, Bašić, Damnjanović, Stevanović, and Stošić used the Kissat SAT solver in a recent paper to systematically determine the small cyclic and ordered Ramsey numbers of several families of graphs. By studying the patterns in their data, Bašić et al. formulated 15 conjectures on cyclic and ordered Ramsey numbers. In this paper, we confirm 9 of their conjectures, trace confirmations of 2 more to existing literature, and, perhaps surprisingly, disprove another one.
ER -