Conjecture that the two repetition ratios agree

For each minimum degree δ4\delta\geq4, let f(δ)f(\delta) and f(δ)f'(\delta) denote the two repetition ratios defined in the paper for the diameter problem under the relevant clique- or chromatic-number condition.

Repetition-ratio conjecture. For every δ4\delta\geq4,

f(δ)=f(δ).f(\delta)=f'(\delta).

The conjecture is motivated by the exact computations for δ=4,5,6\delta=4,5,6, where the optimal repeatable graphs have equal chromatic and clique numbers; the supplied text gives no resolution for general δ\delta.

Sources & referencesView supporting material

Primary source

Stijn Cambie and Jorik Jooken, “Sharp results for the Erdős, Pach, Pollack and Tuza problem”, arXiv:2502.08626 (2025).

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