Eventual exact rainbow saturation conjecture for C5C_5

Let C5C_5 denote the cycle on five vertices, and let rsat(n,C5)rsat(n,C_5) be its rainbow saturation number. Eventual exact rainbow saturation conjecture for C5C_5. There exists N0NN_0\in\mathbb{N} such that, for every nN0n\geq N_0,

rsat(n,C5)=2n6.rsat(n,C_5)=2n-6.

This asserts that the paper's construction for C5C_5 is eventually optimal, making its upper bound the exact value for all sufficiently large orders. The statement is presented as a belief following the paper's bounds; no resolution is supplied.

Sources & referencesView supporting material

Primary source

Yiduo Xu, Zhen He and Mei Lu, “The Rainbow Saturation Number of Cycles”, arXiv:2501.06782 (2025).

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