Keeping it simple, but…

We examine the specialization to simple matroids of certain problems in extremal matroid theory that are concerned with bounded cocircuit size. Assume that each cocircuit of a simple matroid M has at most d elements. We show that if M has rank 3, then M ...

Reid [Every vertex a king, Discrete Math. 38 (1982) 93-98] showed that a non-trivial tournament H is contained in a tournament whose 2-kings are exactly the vertices of H if and only if H contains no transmitter. Let T be a semicomplete multipartite ...

A tournament is simple if the corresponding relational system is simple in the algebraic sense. It is shown that any tournament T"n with n nodes can be embedded in a simple tournament T"n"+"1 apart from two exceptional types of tournaments which can be ...