graphoid.
A matroid that has two collections of nonempty subsets called circuits and cocircuits such that the intersection of any circuit and cocircuit is not only the identity matroid, no circuit properly contains another circuit, no cocircuit properly contains another cocircuit, and for any painting of M that colors exactly one element green and the rest either red or blue there exists either a circuit containing the green element and no red elements or a cocircuit containing the green element and no blue elements.
Meaning & usage
A matroid that has two collections of nonempty subsets called circuits and cocircuits such that the intersection of any circuit and cocircuit is not only the identity matroid, no circuit properly contains another circuit, no cocircuit properly contains another cocircuit, and for any painting of M that colors exactly one element green and the rest either red or blue there exists either a circuit containing the green element and no red elements or a cocircuit containing the green element and no blue elements.
A set of statements of the form, "X is irrelevant to Y given that we know Z" where X, Y and Z are sets of variables, which can be manipulated by a set of axioms concerning informational irrelevance and its graphical representation.
Where this word comes from
From graph + -oid. 1985, United States.
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Definitions, grammatical labels, IPA, etymology and examples: Wiktionary contributors, extracted by Kaikki / Wiktextract. Adapted under CC BY-SA 4.0. Selected fields and authored examples are shown; third-party quotations and audio are omitted. See contributor history.
Last enriched 2026-09-10. Definitions are in English. Romanizations are shown when supplied by the source; syllable estimates are omitted for unsupported scripts.