Math 3330 - Solution set for Assignment 1 - Fall 2011.
1. Let n 2, and G be a simple graph with n vertices. Prove that there are vertices v
and w of G such that deg(v ) = deg(w).
Solution: Let G be a
Math 3330 - Solution to Assignment 5 - Fall 2011.
1. Prove that every graph G has a vertex ordering relative to which the sequential
vertex-coloring algorithm uses (G) colors.
Solution: Let f : VG cfw
MATH 3330 Take Home nal.
Due Wednesday April 16, 4pm in my ofce. Legible copies via e-mail will be accepted.
Groups up to size 3 are allowed.
[16]Q1: In the following graph, where (c,f) =
(capacity, o
Sample 1: In-Class Final
Q1: (a) Let G be a graph. Complete the following denitions.
(a) G is a complete graph if every pair of vertices are joined by an edge
(b) An independent set I of G consists of
MATH 3330 Assignment 1 Solutions
Question 1.
(4 points) Draw a geometric representation for the following graphs:
a) G1 = (cfw_1, 2, 3, 4, cfw_1, 2, cfw_1, 3, cfw_1, 4)
b) G2 = (cfw_a, b, c, d, e, f,
MATH 3330 Assignment 1
Due Friday September 22 in class
Note that your solutions require full justication for full marks.
Question 1.
(4 points) Draw a geometric representation for the following graph
MATH 3330 Assignment 2
Due Friday September 29 in class
Note that your solutions require full justication for full marks.
Question 1.
(10 points)
a) In our denition of a graph, what is the maximum num
Math 3330 - Assignment 2 - Fall 2011.
1. Provide a simple graph as an example for each of the following cases. Provide an
explanation in each case.
(i) A walk that is not a trail.
(ii) A trail that is
Math 3330 - Solution to Assignment 3 - Fall 2011.
1. Prove or disprove each of the following statements:
(i) Every graph with fewer edges than vertices has a component that is a tree.
(ii) If a simple
Math 3330 - Solutions of Assignment 6 - Fall 2011.
1. In each case, either prove the statement or disprove it by providing a counterexample.
(i) Subdividing an edge e in a graph G causes the edge-chro
Assignment 4: Due Wednesday Oct 14.
Q1: Find a minimum weight spanning tree for the following graph using
a) Prims Algorithm. (Show your work by using a table.)
b) Kruskals Algorithm. (It is only requ