Pries Fall 2012: Introduction to Combinatorial Theory: Homework
On these problems, it is ok to work with 2-3 other people as long as each person contributes
actively and writes up the solutions independently. On each assignment, write down the
names of the people you worked with.
Homework 1. Due Friday 8/24. Induction and Introduction to Graphs
Read: LPV 2.1, 7.1
Problems: LPV 2.1.4, 2.1.7, 2.1.9, 7.1.2 bcd, 7.1.5.
Choice of problems: Do either LPV 2.1.8 or 7.1.7.
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Homework 2. Due Friday 8/31.
Read: LPV 7.2, 7.3, HHM 1.1
Problems: LPV 7.3.1, 7.3.3, 7.3.6(ab); HHM S1.1.2 #3(cd); HHM S1.1.3 #1, 3, 9.
Choice of problems: Do either LPV 7.2.11 or HHM S1.1.2 #7.
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Homework 3. Due Monday 9/10.
Read: HHM 1.2
Problems: HHM pg 20-21 #2,3,5,8; HHM pg 25 #1,3,5,9.
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Homework 4. Due Friday 9/28.
Read: HHM 1.3, 1.5
Problems: Trees: HHM pg 33 # 3, pg 37 #2, pg 42 # 5, pg 51 # 2,3,4,5.
Planarity: Draw K5 on a doughnut with no edges crossing. HHM pg 79 # 1,2,4, pg 83 # 2,
pg 85 #2 (careful, there is another # 2 at top of this page).
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Homework 5. Due Monday 10/8.
Read: HHM 1.6
Problems: HHM pg 87 #1df, pg 93 #5, pg 97 #2, pg 101 #1de, 4 and LPV 13.4.5.
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Homework 6. Due Friday 10/19.
Read: HHM 2.1, 2.2, 2.3.
Problems: HHM pg 134 #2,3,10, pg 142 #3, pg 150 #11, pg 170 #5, 6ab.
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Homework 7. Due Friday 11/09.
Read: HHM 2.5, 2.6, handout.
Problems: HHM pg 161 #1, pg 166 #2, Handout pg 245 #5, 8, 13, 14, pg 253 # 1, 14.
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Homework 8. Due Friday 11/16.
Read: HHM 2.6.5.
Problems: HHM pg 184 #6,7(ab).
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Review problems:
HHM pg 166 #3, pg 171 #8, pg 176 #7a, pg 180 #3.
Tucker handout pg 246 #18, pg 253 #3.
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Homework 9. Not collected but on final.
Read: HHM 2.7.2
Problems: HHM pg 200 #3, #4.
A) How many ways are there to 2-color the 64 squares of an 8 × 8 chessboard?
B) How many ways are there to 3-color the 5 horses on a merry-go-round?
C) A domino has 2 adjacent squares, each of which is either blank or has 1-6 dots on it. How
many different dominos are there? Answer this question in two ways: first, using Burnside’s
theorem and then using (unordered) selections with repetition.
D) How many ways are there to color the 5 faces of a pyramid with a square base using 4
colors?