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ams303HW2sol

# ams303HW2sol - AMS 303 Homework#5 ApComb Chapter 9 C1C2 C3...

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AMS 303 Homework #5 ApComb Chapter 9 9.1: 5 c) C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 C 11 C 12 C 13 C 14 C 15 C 16 C 1 C 3 C 2 C 5 C 4 C 6 C 9 C 8 C 7 C 11 C 10 C 15 C 14 C 13 C 12 C 16 ; 10b) π 7 , c) π 2 , 9.2: 3 . 1 3 (3 15 + 2 x 3 5 ) ; 4. 1 4 (2 64 + 2 x 2 16 + 2 32 ) ; 10. 1 2 (3 x 2 n -1 ) , n even, 1 2 (3 x 2 n -1 + 3 x 2 ( n -1 ) /2 ) 9.3: 4a) 315, c) 5934; 5d) 1 4 ( m 8 + 3 m 4 ), e) 1 12 ( m 7 + 2 m 2 + 2 m 3 + 4 m 4 + 3 m 5 ), 7d) 1 4 ( m 10 + m 5 + m 6 + m 7 ) , e) 1 12 ( m 12 + 2 m 2 + 2 m 4 + m 6 + 6 m 7 ) ; 9.4: 2b) 1 9 {( b + w ) 9 +6( b 9 + w 9 )+2( b 3 + w 3 ) 3 }, 10, c) 1 10 {( b + w ) 10 +4( b 10 + w 10 )+4( b 5 + w 5 ) 2 +( b 2 + w 2 ) 5 }, 12, 7d) 1 4 {( b + w ) 10 +( b 2 + w 2 ) 5 }+ ( b + w ) 2 ( b 2 + w 2 ) 4 + ( b + w ) 4 ( b 2 + w 2 ) 3 }, e) 1 12 {( b + w ) 12 +2( b 6 + w 6 ) 2 +2( b 3 + w 3 ) 4 + ( b 2 + w 2 ) 6 + 6( b 2 + w 2 ) 5 ( b + w ) 2 }, 9a) 1 12 {( b + w ) 4 + 8( b 3 + w 3 )( b + w ) + 3( b 2 + w 2 ) 2 }, 9b) 1 24 {( b + w ) 6 + 6( b 4 + w 4 )( b + w ) 2 + 3( b 2 + w 2 ) 2 ( b + w ) 2 + 6( b 2 + w 2 ) 3 + 8( b 3 + w 3 ) 2 }; Homework #6, ApComb Chapter 4 4.3: 2a) max flow = 19, P ={ a , b , d }, b) max flow = 24, P ={ a , b ,c}, 3. max flow = 50, P = { f , z }; 6. yes, build successive flow paths by choosing leftmost unsaturated edge leaving each vertex; 8a) not possible, cut with P ={ a , b , c , d , e , g }has capacity 50, b) now possible; 9. 5, build paths by choosing leftmost unused edge leaving each vertex; 12. split b , c , d each into 2 vertices, one x i for incoming edges and one x o for outgoing edges with an edge of cap. 5 joining the 2 vertices; max flow =12,
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