Seminars in January 2011

• Suho Oh (오수호), Matchings in Bipartite Graphs and the Generalized Permutohedra

  Matchings in Bipartite Graphs and the Generalized Permutohedra

  Suho Oh (오수호)
  Department of Mathematics, MIT, Cambridge, MA, USA

  2011/1/21 Fri 4PM-5PM

  A transversal matroid is a collection of objects that encodes maximal matchings in a bipartite graph. Generalized permutohedra is a class of polytopes obtained by deforming the permutohedron. We introduce a nice bijection that allows one to view transversal matroids as set of lattice points inside a generalized permutohedron. As a corollary, we solve a special case of the 30-year old conjecture by Stanley on matroids and pure O-sequences. The talk will be elementary and purely combinatorial.

  Tags:

  • 오수호

• Ilhee Kim (김일희), Forbidden induced subgraphs of double-split graphs

  Forbidden induced subgraphs of double-split graphs

  Ilhee Kim (김일희)
  Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, USA

  2011/1/7 Fri 4PM-5PM

  In the course of proving the strong perfect graph theorem, Chudnovsky, Robertson, Seymour, and Thomas showed that every perfect graph either belongs to one of five basic classes or admits one of several decompositions. Four of the basic classes are closed under taking induced subgraphs (and have known forbidden subgraph characterizations), while the fifth one, consisting of double-split graphs, is not. A graph is doubled if it is an induced subgraph of a double-split graph. We find the forbidden induced subgraph characterization of doubled graphs; it contains 44 graphs.
  This is joint work with Boris Alexeev, and Alexandra Fradkin.

  Tags:

  • 김일희