  Plural (or multiple-conclusion) cuts are inferences made by applying a
structural rule introduced by Gentzen for his sequent formulation of classical
logic. As singular (single-conclusion) cuts yield trees, which underlie
ordinary natural deduction derivations, so plural cuts yield graphs of a more
complicated kind, related to trees, which this paper defines. Besides the
inductive definition of these oriented graphs, which is based on sequent
systems, a non-inductive, graph-theoretical, combinatorial, definition is
given, and to reach that other definition is the main goal of the paper. As
trees underlie multicategories, so the graphs of plural cuts underlie
polycategories. The graphs of plural cuts are interesting in particular when
the plural cuts are appropriate for sequent systems without the structural rule
of permutation, and the main body of the paper deals with that matter. It gives
a combinatorial characterization of the planarity of the graphs involved.
