### Textbook

Schrijver, Alexander. *Combinatorial Optimization: Polyhedra and Efficiency.* New York, NY: Springer-Verlag, 2003. ISBN: 3540443894.

### Additional References

In addition to the plethora of references in Schrijver’s textbook, here are a few references related to what is covered in lecture. Additional pointers appear in the scribe notes.

Lovász, L., and M. D. Plummer. *Matching Theory.* Vol. 29. *Annals of Discrete Mathematics.* Amsterdam: North-Holland Publishing Co., 1986. [The reference for everything related to matching.]

Oxley, J. G. *Matroid Theory.* New York: Oxford University Press, 1992. [An in-depth discussion of matroid theory.]

Welsh, D. J. A., P. D. Seymour, R. E. Bixby, and W. H. Cunningham. In *The Handbook of Combinatorics.* Vol. 1. Cambridge, MA: MIT Press, 1995, Chapters on Matroids.

Fujishige, S. *Submodular Functions and Optimization.* Vol. 47. *Annals of Discrete Mathematics.* Amsterdam: North-Holland Publishing Co., 1999.

Bessy, S. “Stabilite et decomposition en circuits d’un digraphe.” In *Dissertation.* Universite Lyon I, 2003. [Lectures 7 and 8]

Cunningham, W. H. “Matching, Matroid, and Extensions.” *Mathematical Programming* B91 (2002): 515-542. [Lectures 16 and 17]

Lovász, L. “The Membership Problem in Jump Systems.” *J. Comb. Theory* (B) 70: 45-66. [Lectures 16 and 17]

Frank, A. “Packing Paths, Circuits, and Cuts.” In *Paths, Flows and VLSI-Layout.* Edited by B. Korte, L. Lovász, H. J. Proemel, and A. Schrijver. New York, NY: Springer-Verlag, 1990. [Lectures 22 and 23]

Wagner, D., and K. Weihe. “A Linear-time Algorithm for Edge-disjoint Paths in Planar Graphs.” *Combinatorica* 15 (1995): 135-150. [Lecture 23]