Matroid theory

Abstract

This chapter introduces matroids, gives several basic examples of them, describes the fundamental constructions for matroids. and defines the Tutte polynomial for matroids. • The matroid theory conventions throughout the handbook. • Circuits, independent sets, bases, rank, closure, flats, and hyperplanes. • Examples of matroids including those from graphs, matrices, and linear codes. • Deletion, contraction, duality, direct sum. 2-sum. • The Tutte polynomial of a matroid and its basic properties.