Introduction to Matorid Theory

  • 申立勇
  • Created: 2014-12-08
Introduction to Matorid Theory

 

Course No.216030Y    

Period10    

Credits0.5   

 Course CategoryLecture     

Primary Coverage
Talks 1. Axioms and examples.
Independen systems, matroids, independen sets and basis, rank functions of matroids,
closure operators and closed sets, circuits of matroids, graphic matroids, uniform matorids and representable matroids.
Talk2. Duality and Matroid Minors
More on representable matorids and regular matroids, matroid duality, dual matroid of graphic matorids and representable matorids, matroid contractions and minors. Witney’s 2-isomorphism theorem.
Talk 3. Connectivity
Tutte connectivity of matoirds, other connectivity of matorids, matroid connectivity verses graph connectivity, decomposition of matorids into 1-sums of connected matroids, decomposition of connected matorids into 2-sums of 3-connected matorids. Some of the commonly used techniques in matroid connectivities.
Talk 4. Binary matroids
Different characterizations of binary matroids, Tutte’s excluded minor characterization of binary matorids, othorgonal properties of binary spaces and binary matroids, eulerian, subeulerian, and supereulerian binary matorids, decomposition of 3-connected binaro matroids into the 3-sum of 4-connected binary amtorids, Seymour’s decomposition of regular matorids.
Talk 5. From graphs to matroids
We will introduce some of the latest developments on circuits, flows and uniformly dense matroids, and other research problems uin matorid theory that are motivated by graph theory problems.

References:
1
Oxley, J. G., Matroid Theory, Oxford Science Publishing, New York, 1992.

                                                AuthorHongjian Lai