turkmath.org

For any surface S, there is a finite list of graphs, such that a graph may be embedded in S if and only if it contains none of the graphs in the list as a minor. It is known that there are exactly two minor minimal graphs that are forbidden for the plane and 35 for the projective plane. These are the only complete results for embedding on a surface. Similarly, there are only partial results for the finite list of forbidden minors for graph invariants that, for each fixed k, the graphs with invariant at most k are minor closed. In this talk we consider the edge search number as the graph invariant and give our results on the minor minimal graphs that are forbbidden for the class of graphs that have a fixed edge search number. This is joint work with D. Dyer and D. Dereniovski.