# Inductive tools for connected ribbon graphs, delta-matroids and multimatroids

## TL;DR

This paper extends splitter theorems to complex combinatorial structures like tight multimatroids, delta-matroids, and ribbon graphs, broadening the theoretical framework for these interconnected mathematical objects.

## Contribution

It generalizes the splitter theorem from matroids to tight multimatroids, delta-matroids, and ribbon graphs, providing new theoretical tools for these structures.

## Key findings

- Splitter theorem for tight multimatroids proved
- Corollaries establish splitter theorems for delta-matroids and ribbon graphs
- Generalizes known results for matroids to broader classes

## Abstract

We prove a splitter theorem for tight multimatroids, generalizing the corresponding result for matroids, obtained independently by Brylawski and Seymour. Further corollaries give splitter theorems for delta-matroids and ribbon graphs.