📖 Matroid

A matroid $M = (E, \\mathcal{I})$ consists of a ground set $E$ and a collection $\\mathcal{I}$ of independent sets satisfying: (1) $\\emptyset \\in \\mathcal{I}$, (2) if $I \\in \\mathcal{I}$ and $J \\subseteq I$, then $J \\in \\mathcal{I}$, (3) if $I, J \\in \\mathcal{I}$ with $|I| < |J|$, then $\\exists e \\in J \\setminus I$ with $I \\cup \\{e\\} \\in \\mathcal{I}$.

From: Introduction to Graph Theory

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