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On the lower- and upper bounds of three-colored anti-Ramsey numbers
Abstract
In this paper we study a relatively new Ramsey type graph parameter introduced by my Bachelor's thesis supervisor Nóra Almási, and her Master's thesis supervisor Maria Axenovich. The parameter ξ(G) denotes the largest natural number n, such that there is a red-blue-green edge coloring of Kn, such that in the edge coloring all copies of G represent all three colors. After a brief recap on Ramsey numbers, we precisely define ξ(G), and take a look at its relations to the Ramsey numbers. In the third chapter we establish lower bounds on ξ(G), in the cases G=K5 and G=K6, namely ξ(K5)≥ 19 and ξ(K6)≥ 31.
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BibTeX
@misc{giesz2026lower,
title = {{On the lower- and upper bounds of three-colored anti-Ramsey numbers}},
author = {Máté Giesz},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03878},
eprint = {2611.03878},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03878},
}
RIS
TY - UNPB
TI - On the lower- and upper bounds of three-colored anti-Ramsey numbers
AU - Máté Giesz
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03878
UR - https://arxiv.org/abs/2611.03878
AB - In this paper we study a relatively new Ramsey type graph parameter introduced by my Bachelor's thesis supervisor Nóra Almási, and her Master's thesis supervisor Maria Axenovich. The parameter ξ(G) denotes the largest natural number n, such that there is a red-blue-green edge coloring of K_n, such that in the edge coloring all copies of G represent all three colors. After a brief recap on Ramsey numbers, we precisely define ξ(G), and take a look at its relations to the Ramsey numbers. In the third chapter we establish lower bounds on ξ(G), in the cases G=K_5 and G=K_6, namely ξ(K_5)≥ 19 and ξ(K_6)≥ 31.
ER -