Lectures on matroids

Abstract

This work is based on a se ri es of papers in th e Transac ti ons of th e Am e rican Mathemati ca l S o· cie ty: A homotopy theorem for matroid s, J and lJ , 88,144--174 (1958): and Matroids and graph s, 90, 572-552 (1959). Th ese pap ers se t out a th eo ry of matruid s, wi th s pec ial e mphas is on the co ndition s for a mat roid to rep rese nt a graph. The treat me nt is as ri gorous as t hat in the original pap e rs , but it is hop ed th at th e prese nt work is e asi e r to read , beca use less co nd e nse d. Many th eo re ms origi na ll y proved on ly for "regu lar matroids" hav e bee n ge neralized to th e less res trict ed c lass of " binary" o nes, and th e las t part of th e work ha s bee n improved by the in corporati on of a th eory of "eve n" matroid s.