Sedlar–Škrekovski's mixed metric dimension conjecture

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Let GG be a connected graph that is not a cycle. Write O(G)=V(G)∪E(G)O(G)=V(G)\cup E(G), let dimm⁡(G)\operatorname{dim_m}(G) denote the minimum cardinality of a mixed metric generator of GG, let ℓ(G)\ell(G) be the number of leaves of GG, and let

c(G)=∣E(G)∣−∣V(G)∣+1c(G)=|E(G)|-|V(G)|+1

be its cyclomatic number. Sedlar–Škrekovski's conjecture.

dimm⁡(G)≤ℓ(G)+2c(G).\operatorname{dim_m}(G)\leq \ell(G)+2c(G).

Sedlar and Škrekovski proposed this bound after determining the mixed metric dimension of unicyclic graphs. The conjecture concerns the mixed metric dimension of connected graphs beyond cycles; its resolution is not established in the supplied source.

References

Primary source

Shi Chen and Xuanlong Ma, “Mixed metric dimension of 2-connected graphs”, arXiv:2607.27573 (2026).

Additional references

3 papers in this index state this conjecture (2020–2026). The statement above is taken from the most recent of them; the others are arXiv:2509.00383, arXiv:2012.08590.

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