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An improved lower bound for the packing number of the 2-token graph of the cycle
Abstract
Let F2(Cn) be the $2$-token graph of the cycle Cn and let ρ denote the packing number. Gómez Soto and Ríos-Castro recently proved that ρ(F2(Cn))≥ a(n) for n≥ 19, where a(n) is an explicit expression. In this note, we prove that ρ(F2(Cn)) ≥ ⌊(n(n−2))/10⌋+1 for every n≥ 3, which improves a(n) by one whenever n≡ 0,2pmod10.
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BibTeX
@misc{rivera2026improved,
title = {{An improved lower bound for the packing number of the 2-token graph of the cycle}},
author = {Luis Manuel Rivera},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31991},
eprint = {2609.31991},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31991},
}
RIS
TY - UNPB
TI - An improved lower bound for the packing number of the 2-token graph of the cycle
AU - Luis Manuel Rivera
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31991
UR - https://arxiv.org/abs/2609.31991
AB - Let F_2(C_n) be the $2$-token graph of the cycle C_n and let ρ denote the packing number. Gómez Soto and Ríos-Castro recently proved that ρ(F_2(C_n))≥ a(n) for n≥ 19, where a(n) is an explicit expression. In this note, we prove that ρ(F_2(C_n)) ≥ ⌊(n(n−2))/10⌋+1 for every n≥ 3, which improves a(n) by one whenever n≡ 0,2pmod10.
ER -