The domination–isolation ratio conjecture for cubic graphs

From papers

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.

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Sources & referencesView supporting material

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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