Multimatroids III. Tightness and Fundamental Graphs

This paper continues the study of multimatroids. Here we introduce the subclass of tight multimatroids, which contains the liftings of even delta-matroids, the 3-matroids derived from isotropic systems, the Eulerian 3-matroids associated to 4-regular graphs and the Eulerian 2-matroids associated to evenly directed 4-regular graphs. The local properties of a tight multimatroid in the vicinity of a base are reflected by a fundamental graph, as in matroid theory. We describe how the fundamental graph is transformed when the base is modified. As an application we derive some connectivity properties of tight multimatroids.