Oriented two-dimensional circuits

Abstract

The natural generalization of a directed graph is an oriented complex, a fundamental concept in algebraic topology. Our study of such complexes follows combinatorial rather than topological lines; when an n-circuit is defined for oriented complexes as a structure achieved by a certain minimization process, we are able to pose a question not easily answered by topological methods, but one directly accessible by elementary combinatorial techniques. Indeed, having asked ourselves what structure such n-circuits possess, we were able to find an answer, at least when n = 2.