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 simple graph with n vertices. Then there are n possible
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_1, . . . , (G) be a proper coloring of G. For every
1
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-chromatic number to increase
by at most 1.
(ii) Subdividing
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 graph G has no cut-edge then every vertex of G has eve
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 not a path.
(iii) A closed trail that is not a cycle.
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 a set of vertices no two of which are adjacent
(c) A p
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, ow), what is the maximum ow
possible?
[16]Q2: (a) The Li
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 required to (i) list the edges, (ii) indicate whether they