On matroid intersection adjacency

This paper is devoted to a simple alternative proof for a theorem of Frank and Tardos (Math. Programming 42 (1988) 489) on adjacency of extreme points in the common base polytope of a pair of matroids. The new proof relies merely on the simultaneous base exchange axiom, independent of the linear inequality description of the polytope due to Edmonds (Guy et al. (Eds.), Combinatorial Structures and Their Applications, Gordon and Breach, London, 1970, p. 69).