GRAPH THEORY FINAL EXAMINATION
APPLIED MATHEMATICS AND STATISTICS 550.472/672
SPRING 2011
Instructions (read carefully):
This exam is due on Thursday, June 19 at 12:00 noon. Please bring your paper t
Graph Theory, Spring 2012, Homework 9
1. (West 7.1.1)
Solution:
2. (West 7.1.2)
Solution:
3. (West 7.1.4)
Solution:
4. (West 7.1.9)
Solution:
5. (West 7.1.11)
Solution:
6. (West 7.1.27)
Solution:
Graph Theory, Spring 2012, Homework 7 and Homework 8
Homework 7:
1. (West 5.3.1)
Solution:
2. (West 5.3.3)
Solution:
3. (West 5.3.4)
Solution:
Homework 8:
1. (West 8.3.13)
Solution:
2. (West 8.3.17)
S
Graph Theory, Spring 2012, Homework 5
1. (West 5.1.1)
Solution:
2. (West 5.1.4)
Solution:
3. (West 5.1.7)
Solution:
4. (West 5.1.20)
Solution:
5. (West 5.1.22)
Solution:
Graph Theory Midterm Examination
Applied Mathematics and Statistics 550.472/672
Spring 2012
Instructions.
You have nearly 48 hours to work on this exam. It is due on Friday, March 9 at 3:00 pm.
You s
Graph Theory, Spring 2012, Homework 5
1. (West 3.3.1) Determine whether the graph (on page 145) has a 1-factor.
Solution: The graph does not have a 1-factor.
Proof: Let G be the graph pictured. Let S
Graph Theory, Spring 2012, Homework 3
1. (West 1.2.10)
Prove or disprove:
(a) Every Eulerian bipartite graph has an even number of edges.
This statement is TRUE.
Proof:
Suppose G is an Eulerian bipart
Graph Theory, Spring 2012, Homework 2
1. (West 1.2.22)
Prove that a graph is connected if and only if for every partition of its vertices into two nonempty
sets, there is an edge with endpoints in bot
Graph Theory, Spring 2012, Homework 1
1. (West 1.1.4)
=
From the denition of isomorphism, prove that G H if and only if G H .
=
Proof:
(=)
Suppose G H . Then, there is an isomorphism (which is also a
21-484, Spring 2004, HW 5 Solutions
1. (3.1.21) Let G be an X ,Y -bigraph such that |N (S )| > |S | for every
S X with S = . Prove that for every edge e of G there is a
matching M that contains e and
Math 485, Graph Theory: Homework #4
Stephen G. Simpson
Due Friday, December 4, 2009
The assignment consists of Exercises 3.1.8, 3.1.19, 3.1.24, 3.1.25, 3.2.6, 6.1.12,
6.1.25, 6.1.35, 6.2.6 in the West
Math 38: Graph Theory
Dartmouth College
Spring 2004
Homework #4: Solutions
2.3.2. If T is a minimum-weight spanning tree of a weighted graph G, then the u, v -path in T is not necessarily a minimum-we
Graph Theory, Spring 2012, Homework 10
1. (West 7.2.4)
Solution:
2. (West 7.2.6)
Solution:
3. (West 7.2.7)
Solution:
4. (West 7.2.8)
Solution:
5. (West 7.2.27)
Solution:
6. (West 7.2.33) Prove that a
Graph Theory, Spring 2012, Homework 11
1. (West 6.1.9)
Solution:
2. (West 6.1.20)
Solution:
3. (West 6.1.29)
Solution:
4. (West 6.1.30)
Solution:
5. (West 6.1.34)
Solution:
6. Prove that if a triangul
GRAPH THEORY FUNDAMENTAL DEFINITIONS
JOHNS HOPKINS UNIVERSITY
APPLIED MATHEMATICS & STATISTICS 550.472/672
Standard combinatorial notation:
Z: Set of integers.
N: Set of natural numbers1; i.e., the
Graph Theory Final Examination
Applied Mathematics and Statistics 550.472/672
Spring 2010
Instructions (read carefully):
You have two days to work on this exam based on the date you selected to begin
Graph Theory Midterm Examination
Applied Mathematics and Statistics 550.472/672
Spring 2011
Instructions.
You have 48 hours to work on this exam. It is due on Tuesday, March 15 at 12:00 noon. You
sho
Graph Theory Midterm Examination
Applied Mathematics and Statistics 550.472/672
Spring 2010
Instructions.
You have one day to work on this exam. It is due in class on Wednesday, March 24 at
9:00 a.m.
Graph Theory Midterm Examination
Applied Mathematics and Statistics 550.472/672
Spring 2007
Instructions.
You have one day to work on this exam. You may choose one of the following two plans:
Take t
Graph Theory Midterm Examination
Applied Mathematics and Statistics 550.472/672
Spring 2006
Instructions.
You have 24 hours for this exam. You may pick up this exam from Ms. Bechtel in the
Applied Ma
L A B
B
Rn stands for all (real) n-vectors (columns) and Rmn stands for all (real) m n-matrices.
Usual typographic conventions apply: s R, x Rn , and A Rmn .
We write either x y or x, y for xt y = x1
2 /22/12
Lives Forever Linked Through Kidney Transplant Chain 124 - NYTimes.com
Reprints
This copy is for your personal, noncommercial use only. You can order presentation-ready copies for
distributio
Tutte Matrix and Perfect Matchings
Let G be a graph with V (G) = [n]. Dene the Tutte matrix of G to be the n n-matrix
T (G) with
xi j
if i j and i < j,
[T (G)]i j = x ji if i j and i > j, and
0
other
Proof that Kruskals Greedy Algorithm
Produces a Minimum Weight Spanning Tree
Let G be a connected graph with n vertices and let w : E (G) R.
Suppose that Kruskals algorithm produces the spanning tree
Graph Theory Topics
Topic
Fundamental definitions
Walks, paths, connection
Bipartite graphs
Trees
Eulerian graphs/trails
Matchings and related topics
Connectivity
Vertex coloring
Ramsey's
Welcome to Graph Theory
First Lectures
Applied Mathematics & Statistics 550.472/672
Spring 2012
About The Course
550.472/672 (Graph Theory)
First Lectures
Spring 2012
2 / 53
Who, Where, When, How
Inst