Math 588
Combinatorial Optimization

Instructor:   Jozsef   Balogh
Office: 237 Illini Hall
Phone: (217) 244-1918 (office)
E-mail: jobal@math.uiuc.edu
Time and place: 12:00 pm- 12:50pm MWF, 441 Altgeld Hall
Office hours: by appointment

• Homework 1:  TBC (To Be Collected): Ch 1: 2, 5, 15,     Ch 2: 3, 5, 7, 8, 9, 11, 13,                        DUE:  February 13 (Monday) 
                           
  
• Homework 2: Ch 3: 3, 4,  6, 7, 13, 14, 15,  26,  21;    DUE:  February 27 (Monday)   
  
  
• Homework 3:                ;    DUE:  March 27 (Monday)   
  
  
• Homework 4:  15.2:     3, 5,  6, 8; + (1) Complete the proof of the game "Bridge it", in particular, why player I is not forced to use the edge "e"?   (2) Let G be a connected graph. An F subset of E(G) is UC, if it contains at most one cycle. Prove a covering theorem using graphs from UC. In particular prove that the family of UC is a matroid.  (3) Prove a packing theorem using graphs from UC.  Note: these theorems should be analogues of the Nash-Williams theorems.    DUE:  April 24 (Monday)   
  
  
• Homework 5:  15.2:    4,  9, 10,  17, 18, 19, 20,  22,  24 (a), (b);    DUE:  April 28, Friday,  1:00pm (sharp!)   
  
  
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