Determining a Binary Matroid from its Small Circuits

James Oxley, Charles Semple, Geoff Whittle

Abstract


It is well known that a rank-$r$ matroid $M$ is uniquely determined by its circuits of size at most $r$. This paper proves that if $M$ is binary and $r\ge 3$, then $M$ is uniquely determined by its circuits of size at most $r-1$ unless $M$ is a binary spike or a special restriction thereof. In the exceptional cases, $M$ is determined up to isomorphism.

Keywords


Binary matroids; Circuit-hyperplane relaxations

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