6 problems

Complete-graph graphic-matroid conjecture. For every $n\geq 1$, the graphic matroid $\mathsf{K}_n$ of the complete graph on $n$ vertices is an extremal matroid.

A rank-$r$ matroid is subsequence-interchangeably base orderable (SIBO) if every pair of bases $A$ and $B$ admits orderings $a_1,\ldots,a_r$ of $A$ and $b_1,\ldots,b_r$ of $B$ such…

A matroid $M$ is orderable if it admits an ordering of its circuits with the relevant ordering property, and it is 3-connected and binary in the usual matroid-theoretic senses. Gra…

Graphicness characterization conjecture. The following assertions are equivalent:

Cocircuit-rank conjecture. One has

Let $M$ be a matroid on ground set $E(M)$. A standard ordering of $E(M)$ is an ordering satisfying the standard-ordering conditions defined for the matroid's broken-circuit complex…