Readings

The following textbooks are the main textbooks for the class:

Stanley, R. P. Enumerative Combinatorics. Vol. I and II. Cambridge, UK: Cambridge University Press, 1999. ISBN: 0521553091 (hardback: vol. I); 0521663512 (paperback: vol. I); 0521560691 (hardback: vol. II).

Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998. ISBN: 0387984917.

———. Extremal Graph Theory. New York, NY: Dover, 2004. ISBN: 0486435962.

Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000. ISBN: 3540663134.

The following textbooks can be used as supplemental reading:

Diestel, R. Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1997. ISBN: 3540261834. (Available electronically on the Graph Theory Web site by R. Diestel).

Matousek, J. Lectures on Discrete Geometry (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 2002. ISBN: 0387953736.

The following readings specifically deal with problem 6 from Problem Set 1:

The original paper is here:

Burago, Ju. D., and V. A. Zalgaller. "Polyhedral embedding of a net." Vestnik Leningrad Univ 15 (1960): 66-80. (In Russian)

A recent relatively simple solution:

Maehara, H. "Acute triangulations of polygons." European J Combin 23 (2002): 45-55.

Interestingly enough, if one allows right triangles there exist plentiful literature:

Baker, B. S., E. Grosse, and C. S. Rafferty. "Nonobtuse triangulation of polygons." Discrete Comput Geom 3 (1988): 147-168.

Bern, M., and D. Eppstein. "Polynomial-size nonobtuse triangulation of polygons." Internat J Comput Geom Appl 2 (1992): 241-255; Errata 449-450.

Bern, M., S. Mitchell, and J. Ruppert. "Linear-size nonobtuse triangulation of polygons." Discrete Comput Geom 14 (1995): 411-428.

The following table lists the readings assigned for each lecture.

Corse readings.

Lec #	Topics	Readings
1	Course Introduction Ramsey Theorem	Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998, pp. 182-189. ISBN: 0387984917.
2	Additive Number Theory Theorems of Schur and Van der Waerden	Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000, pp. 326. ISBN: 3540663134. Khinchin, A. Y. Three Pearls of Number Theory. Mineola, NY: Dover Publications, Inc., 1998, section 1. ISBN: 0486400263. (Reprint of the 1952 translation.)
3	Lower Bound in Schur's Theorem Erdös-Szekeres Theorem (Two Proofs) 2-Colorability of Multigraphs Intersection Conditions	Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000, pp. 230, 327, and 65-66. ISBN: 3540663134.
4	More on Colorings Greedy Algorithm Height Functions Argument for 3-Colorings of a Rectangle Erdös Theorem	Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000, pp. 66-67. ISBN: 3540663134. Luby, M., D. Randall, and A. Sinclair. "Markov Chain Algorithms for Planar Lattice Structures." FOCS 1995. (Paper)
5	More on Colorings (cont.) Erdös-Lovász Theorem Brooks Theorem	Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000, pp. 67. ISBN: 3540663134. Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998, pp. 145-149. ISBN: 0387984917.
6	5-Color Theorem Vizing's Theorem	Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998, pp. 146-154. ISBN: 0387984917. ———. Extremal Graph Theory. New York, NY: Dover, 2004, pp. 221-234. ISBN: 0486435962.
7	Edge Coloring of Bipartite Graphs Heawood Formula	Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998, pp. 154-161. ISBN: 0387984917. ———. Extremal Graph Theory. New York, NY: Dover, 2004, pp. 243-254. ISBN: 0486435962.
8	Glauber Dynamics The Diameter Explicit Calculations Bounds on Chromatic Number via the Number of Edges, and via the Independence Number
9	Chromatic Polynomial NBC Theorem
10	Acyclic Orientations Stanley's Theorem Two Definitions of the Tutte Polynomial	Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998, pp. 335-339. ISBN: 0387984917.
11	More on Tutte Polynomial Special Values External and Internal Activities Tutte's Theorem	Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998, pp. 345-354. ISBN: 0387984917.
12	Tutte Polynomial for a Cycle Gessel's Formula for Tutte Polynomial of a Complete Graph	Gessel, I. M. "Enumerative applications of a decomposition for graphs and digraphs." Discrete Math 139, no. 1-3 (1995): 257–271. (Paper)
13	Crapo's Bijection Medial Graph and Two Type of Cuts Introduction to Knot Theory Reidemeister Moves	Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998, pp. 358-363. ISBN: 0387984917. Korn, M., and I. Pak. Combinatorial evaluations of the Tutte polynomial. Preprint (2003) available at Research (Igor Pak Home Page). (Paper)
14	Kauffman Bracket and Jones Polynomial	Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998, pp. 364-371. ISBN: 0387984917.
15	Linear Algebra Methods Oddtown Theorem Fisher's Inequality 2-Distance Sets	Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000, section 14. ISBN: 3540663134.
16	Non-uniform Ray-Chaudhuri-Wilson Theorem Frankl-Wilson Theorem
17	Borsuk Conjecture Kahn-Kalai Theorem	Aigner, M., and G. Ziegler. Proof from the BOOK. 2nd ed. New York, NY: Springer-Verlag, August 1998, pp. 83-88. ISBN: 3540636986.
18	Packing with Bipartite Graphs Testing Matrix Multiplication
19	Hamiltonicity, Basic Results Tutte's Counter Example Length of the Longest Path in a Planar Graph	Diestel, R. Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1997, section 10.1. ISBN 3540261834. (Available electronically on the Graph Theory Web site by R. Diestel).
20	Grinberg's Formula Lovász and Babai Conjectures for Vertex-transitive Graphs Dirac's Theorem	Bollobás, B. Extremal Graph Theory. New York, NY: Dover, 2004, pp. 143-146. ISBN: 0486435962.
21	Tutte's Theorem Every Cubic Graph Contains either no HC, or At Least Three Examples of Hamiltonian Cycles in Cayley Graphs of Sn
22	Hamiltonian Cayley Graphs of General Groups	Pak, I., and R. Radoicic. "Hamiltonian paths in Cayley graphs." Preprint (2002) available at Research (Igor Pak Home Page). (Paper)
23	Menger Theorem Gallai-Milgram Theorem	Diestel, R. Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1997, sections 2.5, and 3.3. ISBN 3540261834. (Available electronically on the Graph Theory Web site by R. Diestel).
24	Dilworth Theorem Hall's Marriage Theorem Erdös-Szekeres Theorem	Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000, pp. 38-39, and 97-100. ISBN: 3540663134.
25	Sperner Theorem Two Proofs of Mantel Theorem Graham-Kleitman Theorem	Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000, pp. 40-41, and 45-46. ISBN: 3540663134.
26	Swell Colorings Ward-Szabo Theorem Affine Planes	Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000, pp. 43-45, and 161-163. ISBN: 3540663134.
27	Turán's Theorem Asymptotic Analogues	Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998, pp. 108-111. ISBN: 0387984917.
28	Pattern Avoidance The case of S3 and Catalan Numbers Stanley-Wilf Conjecture
29	Permutation Patterns Arratia Theorem Furedi-Hajnal Conjecture	Arratia, R. "On the Stanley-Wilf conjecture for the number of permutations avoiding a given pattern." Electron J Combin 6, no. 1 (1999). (Paper)
30	Proof by Marcus and Tardos of the Stanley-Wilf Conjecture	Marcus, A., and G. Tardos. "Excluded permutation matrices and the Stanley-Wilf conjecture." J Combin Theory Ser A 107, no. 1 (2004): 153–160.
31	Non-intersecting Path Principle Gessel-Viennot Determinants Binet-Cauchy Identity	Stanley, R. P. Enumerative Combinatorics. Vol. I. Cambridge, UK: Cambridge University Press, 1999, section 2.7. ISBN: 0521553091 (hardback : vol. I); 0521663512. (paperback : vol. I).
32	Convex Polyomino Narayana Numbers MacMahon Formula	Stanley, R. P. Enumerative Combinatorics. Vol. II. Cambridge, UK: Cambridge University Press, 1999, pp. 378. ISBN: 0521560691 (hardback: vol. II).
33	Solid Partitions MacMahon's Theorem Hook-content Formula	Stanley, R. P. Enumerative Combinatorics. Vol. II. Cambridge, UK: Cambridge University Press, 1999, section 7. ISBN: 0521560691 (hardback: vol. II).
34	Hook Length Formula	Pak, I. "Hook Length Formula and Geometric Combinatorics." Séminaire Lotharingien de Combinatoire 46 (2001): article B46f.
35	Two Polytope Theorem	Pak, I. "Hook Length Formula and Geometric Combinatorics." Séminaire Lotharingien de Combinatoire 46 (2001): article B46f.
36	Connection to RSK Special Cases	Pak, I. "Hook Length Formula and Geometric Combinatorics." Séminaire Lotharingien de Combinatoire 46 (2001): article B46f.
37	Duality Number of Involutions in Sn	Pak, I. "Hook Length Formula and Geometric Combinatorics." Séminaire Lotharingien de Combinatoire 46 (2001): article B46f.
38	Direct bijective Proof of the Hook Length Formula	Novelli, J. C., I. Pak, and A. V. Stoyanovsky. "A direct bijective proof of the hook-length formula." Discrete Mathematics and Theoretical Computer Science 1 (1997): 53-67.
39	Introduction to Tilings Thurston's Theorem	Thurston, W. P. "Conway's tiling groups." Amer Math Monthly 97, no. 8 (1990): 757-773.