FALL 2008: MATH 4022 (Intro to Graph Theory)
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ALL HW PROBLEMS ARE FROM THE BOOK BY Douglas West,
UNLESS SPECIFIED OTHERWISE:
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HOMEWORK 1 (Due: Wednesday, Sept. 3rd)
Section 1.1: Problems 12, 16, 28, 30
Section 1.2: Problems 20, 25, 27
Section 1.3: Problems 41
Optional Problems (no need to turn in): 1.1.25, 1.1.29, 1.2.8
HOMEWORK 2 (Due: Monday, Sept. 15th)
Section 1.3: Problems 8, 64
Section 2.1: Problems 37
Section 2.2: Problems 1, 9, 10, 17
Section 2.3: Problem 7 (Hint should refer to 2.1.37, and not 2.1.34)
TEST 1 (September 22nd)
First three to be done in class;
the FOURTH to be brought back to CLASS
on WEDNESDAY, Sept. 24th
HOMEWORK 3 (Due: Monday, Oct. 6th)
Section 3.1: Problems 3, 28, 33, 37
Section 3.3: Problems 10, 15, 16
HOMEWORK 4 (Due: Monday, Oct. 27th)
Section 4.1: Problems 1, 5, 7, 8, 28
Section 4.2: Problems 1, 8, 24
TEST 2 (October 31st)
First three to be done in class;
the 4th+5th to be brought back to CLASS
on Monday, Nov. 3rd
HOMEWORK 5 (Due: Monday, Nov. 24th)
Section 5.1: Problems 1, 4, 28, 38
Section 5.2: Problems 1, 22 * (see below)
Section 5.3: Problems 1, 8
Extra Problem: An n-set is monochromatic, if every element of the set gets
the same color. A collection of n-sets has Property B, if there exists
a 2-coloring (as in a Red-Blue coloring) of the elements so that no set is
monochromatic. Show that every collection containing less than
2^{n-1} sets (each being an n-set) has Property B.
(Hint: use a random 2-coloring.)
(*) Sorry for the typo: the RANGE should be THREE MILES rather than 6 miles; everything else is good.
Use Application 5.2.11 in the book to solve this.
The problem is adapted (as acknowledged in the textbook) from Bondy-Murty,
where the city has RADIUS 6 MILES and a range of NINE MILES for each transmitting
station.
*** FINAL EXAM on Wednesday, Dec. 10th, 11:30am -- 2:20pm (Room 246)
Syllabus: Chapters 1-- 5 of Doug West's book.
OPEN TEXT BOOK ***