We prove that for any infinite set of graphs of bounded genus, some member of the set is isomorphic to a minor of another. As a consequence, for any surface Σ there is a finite list of graphs, such that a general graph may be drawn in Σ if an only if it topologically contains none of the graphs in the list.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics