Problem Set #2
Due: Thursday, 20 September 2012
Students registered in MATH 401 should submit solutions to three of the following
problems. Students in MATH 801 should submit solutions to all ve.
1. For a positive integer , the boolean lattice is the grap
Problem Set #3
Due: Thursday, 27 September 2012
Students registered in MATH 401 should submit solutions to three of the following
problems. Students in MATH 801 should submit solutions to all ve.
1
1. Let be a graph with at least two vertices, and let ()
Problem Set #5
Due: Thursday, 11 October 2012
Students registered in MATH 401 should submit solutions to three of the following
problems. Students in MATH 801 should submit solutions to all ve.
1. Let be a cycle in a connected weighted graph, and let be a
Problem Set #8
Due: Thursday, 1 November 2012
Students registered in MATH 401 should submit solutions to three of the following
problems. Students in MATH 801 should submit solutions to all ve.
1. Exhibit a perfect matching in the graph below or give a sh
Problem Set #4
Due: Thursday, 4 October 2012
Students registered in MATH 401 should submit solutions to three of the following
problems. Students in MATH 801 should submit solutions to all ve.
1. Let 1 , , be positive integers with 2. Prove that there exi
Problem Set #11
Due: Thursday, 22 November 2012
Students registered in MATH 401 should submit solutions to three of the following
problems. Students in MATH 801 should submit solutions to all ve.
1. (a) Calculate the chromatic polynomial of 1,3 by using t
Problem Set #12
Due: Thursday, 29 November 2012
Students registered in MATH 401 should submit solutions to three of the following
problems. Students in MATH 801 should submit solutions to all ve.
1. For the graph below, prove it is nonplanar or provide a