2005 Midterm

2005 Midterm - Networked Life CSE 112 Prof. Michael Kearns...

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Networked Life CSE 112 Prof. Michael Kearns Midterm Examination March 3, 2005 NAME: ___________________________________ PENN ID: __________________________________ Exam Score: Problem 1:__________/12 Problem 2:__________/12 Problem 3:__________/24 Problem 4:__________/10 Problem 5:__________/12 Problem 6:__________/10 Problem 7:__________/12 Problem 8:__________/8 TOTAL:____________/100
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1. (12 points) Consider the table below, reproduced from Watts. (a) (6 points) Briefly but precisely describe each of the three networks mentioned in the table. Give definitions for the vertices, and for the edges. (b) (6 points) Describe the major conceptual points that Watts is summarizing in this table. You should refer to specific quantities and values in the table in your description.
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specified list of properties. Keep your examples as simple as possible (points may be deducted for excessive complexity). Clearly annotate your drawing in a way that indicates why the graph has each of the requested properties. a. (3 points) An undirected graph with worst-case diameter 5, chromatic number (minimum number of colors) equal to 3, and a maximum independent set of size 3. b. (3 points) An undirected graph with a perfect matching and chromatic number 4. c. (3 points) An undirected graph that is planar, has no cliques of size 3, and has chromatic number 3. d. (3 points) An undirected graph that is planar, connected, has a clique of size 3, and an
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2005 Midterm - Networked Life CSE 112 Prof. Michael Kearns...

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