The circuits containing some fixed element of a connected matroid (such a collection is called a port) provide a matroid generalization of the "path collections" of graphs. In this note we show how to translate forbidden minor theorems in matroid theory into results about ports - and we find that many theorems are strengthened by such translation. Those collections of sets which are "path collections" of graphs may then be characterized.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics