Computational Lower Bounds for Wheel Ramsey Numbers

We study small off-diagonal Ramsey numbers involving wheel graphs. Following Radziszowski’s convention, we write Wn=K1+Cn−1 for the wheel on n vertices. A lower bound for R(Wm,Wn) is certified by a graph G such that G is Wm-free and G¯ is Wn-free. We conduct computational experiments using several complementary search techniques, including partial Ramsey colorings and local search procedures. The computations exploit the structure of wheels: G contains Wn if and only if some vertex neighborhood contains a cycle Cn−1. We report new lower-bound constructions for three off-diagonal wheel Ramsey numbers and provide the corresponding Ramsey graphs as explicit certificates.

Authors

Institutions

Publication Details

Journal
Mathematics
Published
2026-06-30
DOI
https://doi.org/10.3390/math14132310
Primary Topic
Limits and Structures in Graph Theory
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Computational Lower Bounds for Wheel Ramsey Numbers

Sergey Bereg
Mathematics
Limits and Structures in Graph Theory
article

Computational Lower Bounds for Wheel Ramsey Numbers

Sergey Bereg
article en

Abstract

We study small off-diagonal Ramsey numbers involving wheel graphs. Following Radziszowski’s convention, we write Wn=K1+Cn−1 for the wheel on n vertices. A lower bound for R(Wm,Wn) is certified by a graph G such that G is Wm-free and G¯ is Wn-free. We conduct computational experiments using several complementary search techniques, including partial Ramsey colorings and local search procedures. The computations exploit the structure of wheels: G contains Wn if and only if some vertex neighborhood contains a cycle Cn−1. We report new lower-bound constructions for three off-diagonal wheel Ramsey numbers and provide the corresponding Ramsey graphs as explicit certificates.

MathematicsVol. 14(13)
The University of Texas at Dallas (US)
Sustainable cities and communities
Openalex Percentile: Top 3%
Limits and Structures in Graph Theory
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.