f2006Solns10 - ECE 190 - Fall, 2006 Assignment 10 Solutions...

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ECE 190 — Fall, 2006 Assignment 10 Solutions 1. a) Only K 2 is bipartite. K 1 is not considered to be bipartite — there is only one vertex so we cannot place the vertices in two non-empty sets. For n 3, K n will always contain a triangle so it cannot be bipartite. b) Here n must be even and greater than or equal to four. We require that n 3 for C n to be de±ned. If n is even, then every second vertex can be placed in one set and the others can be placed in a second set. If n is odd, this cannot be done. c) For no value of n is W n bipartite. Every wheel contains triangles. d) Q n is bipartite for all n 1. To demonstrate this, note that we can associate each vertex in Q n with a bit string of length n , with adjacent vertices differing by only one bit. Place all vertices with an even number of zero bits in one set and those with an odd number of zero bits in the other set. 2. a) K n has n vertices. It has ( n 2 ) = n 2 - n 2 edges.
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This homework help was uploaded on 04/19/2008 for the course ECE 190 taught by Professor Carter during the Fall '06 term at University of Toronto- Toronto.

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f2006Solns10 - ECE 190 - Fall, 2006 Assignment 10 Solutions...

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