## Topics in Discrete Mathematics: Structural Graph Theory

#### Math 958 Fall 2011 Section 001

Announcements:
(Dec 16) I have finished grading the final homework and calculating the final course grades. I have recorded these grades both on MyRed and Blackboard. I will put the homework in peoples' mailboxes in the math department office. Please let me know if you have any questions.
I really enjoyed teaching this class, and I hope that you enjoyed it, too. Thanks for your interest during the semester, and have a great winter break!

Course Materials:
Course information and course log recording topics covered in each lecture.
Textbook: Textbook: Preliminary version of Volume II: Structure of Graphs from The Art of Combinatorics by Douglas B. West. Supplemental text: Graph Theory by Reinhard Diestel.

Homework:
 homework #1, due Fri Sept 16 homework #2, due Wed Oct 19 homework #3, due Mon Nov 21 homework #4, due Wed Dec 14

Papers to present:
• (Lauren Keough) H. Kaul and A. Kostochka, Extremal graphs for a graph packing theorem of Sauer and Spencer. Combin. Probab. Comput. 16 (2007), no. 3, 409–416. MR2312435
• (Sarah Behrens) G. Sierksma and H. Hoogeveen, Seven criteria for integer sequences being graphic. J. Graph Theory 15 (1991), no. 2, 223-231. MR1106533; G. Isaak and D. B. West, The edge-count criterion for graphic lists. Electron. J. Combin. 17 (2010), no. 1, Note 36, 5 pp. MR2769105
• D. R. Fulkerson, A. J. Hoffman, and M. H. McAndrew, Some properties of graphs with multiple edges. Canad. J. Math. 17 1965 166-177. MR0177908; S. Kundu, A factorization theorem for a certain class of graphs. Discrete Math. 8 (1974), 41-47. MR0335357
• (Jeremy Trageser) M. D. Barrus, S. G. Hartke, K. F. Jao, and D. B. West, Length thresholds for graphic lists given fixed largest and smallest entries and bounded gaps. Discrete Math., to appear. pdf
• (Derrick Stolee) Z. Ryjáček, On a closure concept in claw-free graphs. J. Combin. Theory Ser. B, 70 (1997), no. 2, 217–224. MR1459867
• (Nora Youngs) M. O. Albertson, You can't paint yourself into a corner. J. Combin. Theory Ser. B, 73 (1998), no. 2, 189–194. MR1632011
• (James Carraher) S. Har-Peled, A simple proof of the existence of a planar separator, preprint on arXiv
• D. W. Cranston and G. Yu, A lower bound on the density of vertex identifying codes for the infinite hexagonal grid. Elec. J. of Combin. Vol. 16, (2009) #R113. MR2546316

Instructor:
Stephen Hartke, hartke @ No . Spam . mäth . únl . edu (appropriately changed)
Office: Avery Hall Room 339, Phone: 402-472-7001
Office Hours: To be announced, or by appointment.
Meeting Times:
Mon, Wed, and Fri, 9:30am-10:20pm, Burnett Hall Room 204

Old Announcements:
(Nov 14) We will not have class on Fri Dec 2.
(Sep 20) We will not have class on Monday October 3.