- Series
- Graph Theory Seminar
- Time
- Thursday, March 17, 2011 - 12:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Arash Asadi – Math, GT
- Organizer
- Robin Thomas

The property that a graph has an embedding in projective plane is closed
under taking minors. So by the well known theorem of Robertson and Seymour,
there exists a finite list of minor-minimal graphs, call it L, such that a
given graph G is projective planar if and only if G does not contain any
graph isomorphic to a member of L as a minor. Glover, Huneke and Wang found
35 graphs in L, and Archdeacon proved that those are all the members of L.
In this talk we show a new
strategy for finding the list L. Our approach is based on conditioning on
the connectivity of a member of L. Assume G is a member of L. If G is not
3-connected then the structure of G is well understood. In the case that G
is 3-connected, the problem breaks down into two main cases, either G has an
internal separation of order three or G is internally 4-connected . In this
talk we find the set of all 3-connected minor minimal non-projective planar
graphs with an internal 3-separation.
This is joint work with Luke Postle and Robin Thomas.