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Unformatted text preview: MATH 682 Problem Set #5 This problem set is due at the beginning of class on April 6 . Below, graph means simple finite graph except where otherwise noted. 1. (10 points) Complete the proof that the Harary graphs are kconnected. You may use the case presented in class of even values of k , either by citation or imitation. (a) (5 points) Show that H n,k is kconnected for even n and odd k . This graph is symmetric, so you may specifically demonstrate connectedness between v 1 and an arbitrary v i in H n,k S for v 1 ,v i 6 S and  S  < k . (b) (5 points) Show that H n,k is kconnected for odd n and odd k . This graph is not symmetric, so you must distinguish between the cases where v 1 S and v 1 / S . 2. (15 points) Answer the following questions about Tur an numbers and extremal graphs. (a) (5 points) Show that the extremal number ex( n,K 1 ,r ) is ( r 1) n 2 if r is odd or n is even, and ( r 1) n 1 2 if r is even and n is even....
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This note was uploaded on 01/12/2012 for the course MATH 682 taught by Professor Wildstrom during the Spring '09 term at University of Louisville.
 Spring '09
 WILDSTROM
 Math

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