Professor Kindred
Math 104 Graph Theory
Homework 5 Solutions
February 28, 2013
Introduction to Graph Theory, West
Section 3.3 10, 16, 22
Section 4.1 9, 25
Section 4.3 2
Problems you should be able to
Professor Kindred
Math 104, Graph Theory
Homework 6 Solutions
March 7, 2013
Introduction to Graph Theory, West
Section 4.2 4, 14
Section 4.3 7, 10, 14
Problems you should be able to do: 4.2.12, 4.3.8
Professor Kindred
Math 104, Graph Theory
Homework 2 Solutions
February 7, 2013
Introduction to Graph Theory, West
Section 1.2: 26, 38, 42
Section 1.3: 14, 18
Section 2.1: 26, 29, 30
DO NOT RE-DISTRIBU
The University of Sydney
MATH 2009
GRAPH THEORY
1.
(a)
(b)
2004
Tutorial 11 Solutions
5
Use the labelling procedure to
find a maximal flow in the
given transport network.
3
A
8
1
2
List all cuts, the
The University of Sydney
MATH 2009
Graph Theory
1.
Tutorial 1
2004
Draw a picture of each of the following graphs, and state whether or not it is
simple.
(a)
(b)
(c)
G1 = (V1 , E1 ), where V1 = cfw_a,
The University of Sydney
MATH2009
GRAPH THEORY
1.
2004
Tutorial 4 Solutions
Find a solution to the Chinese
Postman Problem in this graph,
given that every edge has equal
weight.
Solution.
The problem
The University of Sydney
MATH 2009
GRAPH THEORY
1.
Tutorial 10 Solutions
2004
In a tournament, the score of a vertex is its out-degree, and the score sequence
is a list of all the scores in non-decrea
Professor Kindred
Math 104, Graph Theory
Homework 4 Solutions
February 21, 2013
Introduction to Graph Theory, West
Section 3.1 18, 21, 25, 40, 42
Problems you should be able to do: 3.1.8, 3.1.29, 3.1.
Professor Kindred
Math 104, Graph Theory
Homework 3 Solutions
February 14, 2013
Introduction to Graph Theory, West
Section 2.1: 37, 62
Section 2.2: 6, 7, 15
Section 2.3: 7, 10, 14
DO NOT RE-DISTRIBUTE
The University of Sydney
MATH 2009
GRAPH THEORY
1.
2004
Tutorial 9 Solutions
Find (G) and 0 (G) in each of the following cases.
(i )
G = K9
(ii ) G = K10
(iii ) G = K5,6
(iv ) G =
Solution.
(i )
For a
The University of Sydney
MATH2009
GRAPH THEORY
1.
Tutorial 5 Solutions
2004
Draw all the spanning trees of this graph:
Solution.
Since the graph has 5 vertices, a spanning tree will have 4 edges. So t
Professor Kindred
Math 104 Graph Theory
Homework 8 Solutions
April 11, 2013
Introduction to Graph Theory, West
Section 7.1 21, 26
Section 6.1 25, 26, 30
Problems you should be able to do: 6.1.4, 6.1.1
Midterm II Version A
CSE 191
Solution
Nov 7, 2014
12:00 - 12:50pm
First Name (Print):
Last Name (Print):
UB ID number:
1. This is a closed book, and closed neighbor exam. You may use a calculator, and
Midterm II Version B
CSE 191
Solution
Nov 7, 2014
12:00 - 12:50pm
First Name (Print):
Last Name (Print):
UB ID number:
1. This is a closed book, and closed neighbor exam. You may use a calculator, and
The University of Sydney
MATH 2009
GRAPH THEORY
1.
(i )
2004
Tutorial 7 Solutions
Let G be the disconnected planar graph shown.
Draw its dual G , and the dual of the dual (G ) .
(ii ) Show that if G i
The University of Sydney
MATH2009
GRAPH THEORY
1.
(i )
2004
Tutorial 6 Solutions
How many Hamiltonian cycles
are there in this graph?
9
7
8
7
9
X
5
9
6
6
7
(ii ) Delete the vertex labelled X (and its
Christina Fragouli
Graph Theory
Exercises for Lectures 8
Thursday, April 30, 2009
Exercise 8.1.
You are asked to design a VLSI network to connect n = 16 devices (such as processor cores,
memories etc)
The University of Sydney
MATH 2009
GRAPH THEORY
1.
2004
Tutorial 3 solutions
Show that the graph on the left is Hamiltonian, but that the other two are not.
Solution.
To show that the graph is Hamilto
Professor Kindred
Math 104, Graph Theory
Homework 9 Solutions
April 18, 2013
Introduction to Graph Theory, West
Section 6.1 33 (modified)
Grid graph problem
Section 6.3 6, 12, 32
Genus of complete gra
The University of Sydney
Pure Mathematics
MATH2009 GRAPH THEORY
Assignment 1
2004
This assignment is due by 1pm Friday 27 August.
Your assignment should be handed in to Carslaw room 521. Do NOT put yo
The University of Sydney
MATH 2009
GRAPH THEORY
1.
2004
Tutorial 12 Solutions
A building contractor advertises for a bricklayer, a carpenter, a plumber and
a toolmaker. He has five applicants one for
The University of Sydney
Pure Mathematics
MATH2009 GRAPH THEORY
Assignment 2
2004
This assignment is due by 1pm Friday 8 October.
Your assignment should be handed in to Carslaw room 521. Do NOT put yo
The University of Sydney
MATH2009
GRAPH THEORY
1.
2004
Tutorial 2
For each of the following sequences of vertices,
state whether or not it represents a walk, trail,
path, closed walk, closed trail, or
The University of Sydney
MATH 2009
GRAPH THEORY
1.
Hubert keeps five varieties (A, B, C, D, E) of
snakes in boxes in his apartment. Some varieties
attack other varieties, and cant be kept together.
In
Professor Kindred
Math 104, Graph Theory
Homework 1 Solutions
January 31, 2013
Introduction to Graph Theory, West
Section 1.1: 14, 15, 23(c), 31
Section 1.2: 22
Section 1.3: 17
DO NOT RE-DISTRIBUTE TH
Christina Fragouli
Graph Theory
Exercises for Lecture 3
Thursday, March 5, 2009
Exercise 3.1. (Proposition 1.7 from Lecture notes 1) Show that if a graph G = (V, E) has
2n vertices and n2 + 1 edges, t
Christina Fragouli
Graph Theory
Exercises for Lecture 5
Thursday, March 19, 2009
Exercise 5.1. Let v and w be two distinct vertices of a de Bruijn digraph such that there exists an
edge that connects
Christina Fragouli
Graph Theory
Exercises for Lecture 4
Thursday, March 12, 2009
Exercise 4.1.
i. Let G = (V, E) be a graph and = minvV deg(v). Show that every simple graph G contains
a path of length