mdm12Section1_5_OddSolutionsFinal

mdm12Section1_5_OddSolutionsFinal -...

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Unformatted text preview: Q1-3Q5-7Q9Q11-13Q15-21Q23CHAPTER 1 Section 1.5, pp. 4952 Solutions to Odd Number Problems1.a)deg(A) = 2, deg(B) = 2, deg(C) = 3, deg(D) = 2, deg(E) = 3 Since there are exactly two vertices of odd degree, the network is traceable. b)deg(P) = 4, deg(Q) = 5, deg(R) = 3, deg(S) = 4, deg(T) = 5, deg(U) = 3. Since there are more than two odd vertices, the network is not traceable. 3.a)Since no more than three provinces/territories (British Columbia, Yukon, Northwest Territories) are adjacent at one time, three colours are needed. b)Since the U.S.A. creates a fourth adjacent area, four colors are needed. Top5.In the existing network 1: deg(A) = 3, deg(B) = 5, deg(C) = 3, deg(D) = 3. It is possible to make the network traceable by adding a bridge joining the two regions A and C. In this new network 2: deg(A) = 4, deg(B) = 5, deg(C) = 3, deg(D) =4. Hence there are only two vertices of odd degree, making the network traceable....
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mdm12Section1_5_OddSolutionsFinal -...

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