Graphs and Matroids Seminar - Ahmad Abdi

Title: Extended odd holes and their blockers

Abstract:

A delta is a clutter whose members are {1,2},{1,3},...,{1,n},{2,3,...,n} where n is at least 3. An extended odd hole is a clutter whose minimum cardinality members are {1,2},{2,3},...,{n-1,n},{n,1} where n is odd and at least 5. Deltas, extended odd holes, and their blockers are basic classes of non-ideal clutters.

Let C be a clutter over n elements where every member has cardinality at least (n+1)/2, and no element is used in every member. Then C has a minor that is either a delta or the blocker of an extended odd hole.

I will sketch the proof of this result. Joint work with Dabeen Lee.