The domination–isolation ratio conjecture for cubic graphs

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Let GG be a cubic graph, with domination number γ(G)\gamma(G) and isolation number ι(G)\iota(G). Domination–isolation ratio conjecture. For every cubic graph GG,

γ(G)≤2ι(G).\gamma(G) \le 2\iota(G).

The conjecture would improve the general ratio bound discussed in the source, which is at most 15/715/7 for cubic graphs; no resolution is given, so the question remains open.

References

Primary source

Geoffrey Boyer, Wayne Goddard and Michael A. Henning, “On the Relationships between Domination, Isolation, and Packing”, arXiv:2606.18172 (2026).

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