Math 580A: Topics in Combinatorial Analysis
Graduate Study Seminar in Matroids and Biased Graphs
(This syllabus is enough for more than a semester!)
- Oxley, Matroid Theory, Chapter 7.
- ``Biased graphs. II. The three matroids'': Sections 2-3.
- ``The Möbius function and the characteristic polynomial''.
- ``The Geometry of Root Systems ...''.
- ``Biased graphs. III. Chromatic and dichromatic invariants'': most of Sections 3-6.
- Oxley, Chapter 9 on binary matroids.
- ``Biased graphs. IV. Geometrical realizations''.
- Oxley, Chapter 13 on regular matroids: parts.
- ``Biased graphs. V. Group and biased expansions''.
- Projective geometry:
Robin Hartshorne, Foundations of Projective Geometry, Benjamin, New York, 1967. Recommended for general projective geometry for the purposes of matroid theory: treats all fields (and division rings) and abstract axiomatization, but without excessive attention to the special theory of nondesarguesian planes.
- Chordal graphs:
Martin Charles Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980. Section 4.2 is recommended for basic information on chordal graphs, which he calls triangulated graphs.
For the matroid theory of chordal graphs, especially the fact that G(Gamma) is supersolvable if and only if Gamma is chordal, see R. P. Stanley, Supersolvable lattices, Algebra Universalis 2 (1972), 197--217; MR 46 #8920.