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Unformatted text preview: MATH 2602 ~ Quiz # 5 — Jone 17, 2009 Name: Each problem is worth 10 points. Show all of your work, and try to be as neat as
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so “the answer<3 No. MATH 2602 — Quiz # 5 — June 17, 2009 Name: Each problem is worth 10 points. Show all of your work, and try to be as neat as
possible. Points may be deducted if solutions are unclear. Use the back of the paper if you need more Space. Problem 1. Prove that every simple graph G with n oertices contains at least two eerttees
with the some degree. (Hint 1: Use pigeonhole principle. Hint 2: This problem shouid seem familiar!) ASSUW‘E ﬂwrre QMKFK \llweVUDj') “3) dffilv):bl do (w): h—i w View Luis ‘3“‘W\;'<"5> m “3‘ ‘ (“003‘s md‘meme ‘L‘fb @ﬁ‘gbﬂf‘kﬁx) WﬂkV%\\C‘3§\bvy‘:‘D Ag my: Hoax/1'33 fox Q3 \iCVCQ) m“ $9 MDE‘CC’r‘f‘Qi 1%? e,.Me(\j \IEVCKQ. EHMQ( was AHWQ We ”0. next—“Q95
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«\\Q (a ewe Amo' eeﬂjh‘ces A WW? Seemedeﬁreﬁ Problem 2. Consider the ﬂoor plan of a museum below. Each fetter represents a room. M U SﬁU M The marking on the walls are the doors from mom to room. _
(a) Represent the floor plan as a graph. What is your vertex set? What is your edge set? (5) Is your graph bipartite“? If so, what is the desired partition {that is, what are Vl and
Vg)? If not, why? (6) Imagine the entrance and can't to the museum are through mam A. Is it possible to
enter the museum, walk through each domey exactly once, and then exit the museum? If so, Show how you 2:10qu accomplish this. If not, give a mathematical reason. ...
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 Spring '09
 COSTELLO
 Math

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