MATH 350: Graph Theory and Combinatorics. Fall 2013.
Due in class on Thursday, October 3rd.
Assignment #1: Paths, Cycles and Trees.
1.
For each of the following statements decide if it is true or false, and
either prove it or give a counterexample.
a) If
MATH 350: Graph Theory and Combinatorics. Fall 2013.
Due in class on Thursday, November 7th.
Assignment #3: Network ows and Ramseys theorem.
1.
Let G be a directed graph and for each edge e let (e) 0 be an
integer, so that for every vertex v ,
(e)
(e) =
e
MATH 350: Graph Theory and Combinatorics. Fall 2013.
Assignment #3: Network ows, covers and Ramseys theorem.
Let G be a directed graph and for each edge e let (e) 0 be an
integer, so that for every vertex v ,
(e) =
(e)
1.
e (v )
e + (v )
Show there is a l
MATH 350: Graph Theory and Combinatorics. Fall 2013.
Due in class on Monday, October 21st.
Assignment #2: Bipartite graphs, matchings and connectivity.
1.
Show that every loopless graph G contains a bipartite subgraph with
at least E (G)/2 edges.
2.
Let
v
u
w
Figure 1: Counterexample for Problem 1a).
MATH 350: Graph Theory and Combinatorics. Fall 2013.
Assignment #1: Paths, Cycles and Trees. Solutions.
1.
For each of the following statements decide if it is true or false, and
either prove it or give a co
MATH 350: Graph Theory and Combinatorics. Fall 2013.
Assignment #2: Bipartite graphs, matching and connectivity.
1.
Show that every loopless graph G contains a bipartite subgraph with
at least E (G)/2 edges.
Solution: Let a partition (A, B ) of V (G) be
MATH 350: Graph Theory and Combinatorics. Fall 2013.
Assignment #4: Matchings and coloring. Solutions.
1. Let G be a graph and Z V (G). Show that the following are equivalent:
(i) G has a matching covering Z , and
(ii) for every X V (G) there are at most
MATH 350: Graph Theory and Combinatorics. Fall 2013.
Due in class on Thursday, November 21st.
Assignment #4: Matchings and coloring.
1. Let G be a graph and Z V (G). Show that the following are equivalent:
(i) G has a matching covering Z , and
(ii) for ev
Math 350 Mock Final. Fall 2013.
Q1 Let G be the graph pictured on Figure 1.
a) Is G planar?
b) What is the maximum integer k , such that G is k connected?
c) Find (G).
d) Find (G).
Q2 Let G be the graph with weights w : E (G) Z+ be the graph pictured
on
Name
MATH 350: Graph Theory and Combinatorics. Fall 2012
Midterm Exam
Thursday, October 11th, 2012, 16:3517:25

The questions have to be answered in the booklets provided. Write your
answers clearly. Justify all your answers. You can consult your notes
MATH 350: Graph Theory and Combinatorics. Fall 2013.
Assignment #5: Planar graphs. Solutions.
1.
A graph G is outerplanar if it can be drawn in the plane so that
every vertex is incident with the innite region. Show that a graph G is
outerplanar if and on
MATH 350: Graph Theory and Combinatorics. Fall 2013.
Due in class on Tuesday, December 3rd.
Assignment #5: Planar graphs.
1.
A graph G is outerplanar if it can be drawn in the plane so that
every vertex is incident with the innite region. Show that a grap