The central-circuit characterization of maximal irreducible hedrites

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Let ii be the number of faces of an irreducible ii-hedrite, and let a central circuit be a central circuit of the hedrite. An irreducible ii-hedrite is maximal irreducible when it cannot be extended while remaining irreducible. Central-circuit characterization. An irreducible ii-hedrite is maximal irreducible if and only if it has i−2i-2 central circuits.

The surrounding discussion gives examples of irreducible ii-hedrites with i−2i-2 central circuits for the relevant values of ii, and notes that these examples are pure. The parser supplies no evidence resolving the stated characterization, so its status remains open.

References

Primary source

M. Deza, M. Dutour and M. Shtogrin, “4-valent plane graphs with 2-, 3- and 4-gonal faces”, arXiv:math/0212351 (2003).

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