Characterizing matroids whose bases form graphic delta-matroids

Abstract

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.

41 pages, 4 figures; revised

References in corpus (2)

• On the interplay between embedded graphs and delta-matroids
• Rank-width and Well-quasi-ordering of Skew-Symmetric or Symmetric Matrices