AMS303/HW7/HW7.md

HW7

Chapter 5

• • 1. k(k-1)(k-2)(k-3)(k-4)(k-5) 7!
  • 2. k(k-1)^5 7*6^5
• • 1. k(k-1)^5+k(k-1)(k-2)^5
  • 2. k(k-1)^4-(k(k-1)^3-k(k-1)(k-2))
• 25. 

• 28. Graph	Lower	Upper	Actual
      C_5	2	3	3
      K_8	7	8	7
      K_{4,6}	6	7	6

• 31. Degree = 3, Color>=3
      Form a Hamiltonian path, color it with 2 colors(total vertices must be even(2m = sum(deg))), and the remaining with the 3rd color