PreprintCC BY 4.0arXiv
The 3-Color 2-Chromatic Gallai-Ramsey Number for Complete Graphs
Abstract
For 1≤ i≤ j≤ k, let gr32(Ki, Kj, Kk) be the least n∈ ℕ such that every rainbow triangle-free $3$-coloring of Kn (using red, blue, and green) contains a red/blue Ki, a red/green Kj, or a blue/green Kk. In this paper, we completely evaluate gr32(Ki, Kj, Kk) for all values of i, j, and k in which r(Ki,Kj) is known.
Related
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BibTeX
@misc{budden20263color,
title = {{The 3-Color 2-Chromatic Gallai-Ramsey Number for Complete Graphs}},
author = {Mark Budden and Elijah DeJonge},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41971},
eprint = {2610.41971},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41971},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The 3-Color 2-Chromatic Gallai-Ramsey Number for Complete Graphs
AU - Mark Budden
AU - Elijah DeJonge
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41971
UR - https://arxiv.org/abs/2610.41971
AB - For 1≤ i≤ j≤ k, let gr^3_2(K_i, K_j, K_k) be the least n∈ ℕ such that every rainbow triangle-free $3$-coloring of K_n (using red, blue, and green) contains a red/blue K_i, a red/green K_j, or a blue/green K_k. In this paper, we completely evaluate gr^3_2(K_i, K_j, K_k) for all values of i, j, and k in which r(K_i,K_j) is known.
ER -