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We introduce delta-graphic matroids, which are matroids whose bases form graphic delta-matroids. The class of delta-graphic matroids contains graphic matroids as well as cographic matroids and is a proper subclass of the class of regular matroids. We give a structural characterization of the class of delta-graphic matroids. We also show that every forbidden minor for the class of delta-graphic matroids has at most $48$ elements.
For an abelian group $Gamma$, a $Gamma$-labelled graph is a graph whose vertices are labelled by elements of $Gamma$. We prove that a certain collection of edge sets of a $Gamma$-labelled graph forms a delta-matroid, which we call a $Gamma$-graphic d
The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and lifted-graphic matroids introduced earlier by Zaslavsky. For each biased graph $(G, mathcal B)$ Zaslavsky de
We give upper and lower bounds on the number of delta-matroids, and on the number of even delta-matroids.
Let $M$ be a 3-connected matroid and let $mathbb F$ be a field. Let $A$ be a matrix over $mathbb F$ representing $M$ and let $(G,mathcal B)$ be a biased graph representing $M$. We characterize the relationship between $A$ and $(G,mathcal B)$, settlin
We investigate valuated matroids with an additional algebraic structure on their residue matroids. We encode the structure in terms of representability over stringent hyperfields. A hyperfield $H$ is {em stringent} if $aboxplus b$ is a singleton un