Notes for 640-428 Graph Theory (Now with colors!)
Instructor: Grigor Sargsyan
11/08/2012
Reminder Exam next Thursday, Grigor will be gone for the exam and following Monday
B&N Tonight 7-9pm
HW 10
Disproven by Example:
Observe that in both, there is exactl
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyoun
Wenzong Zhao
09/13/2012
Quiz Monday, pick problems from homework
Theorem : Every graph of order n 3 and size m >
n2
4
contains a triangle.
Proof. The claim is true for n = 3, n = 4.
We want to pr
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyoun
Wenzong Zhao
09/10/2012
webpage: math.rutgers.edu/ gs481/courses.html
There is a syllabus.
Oce hours this week: Thursday 2-3:30
First quiz: next Monday
Book has a lot of information and denitions
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Solutions, Problem Set 2, part II; Math 428, Fall 2007
2A. Let W be a closed walk in a multiigraph and assume that W does not contain a cycle.
Prove that some edge of W occurs twice in succession.
We do a proof by induction. Let Sk be the statement that i
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Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyoun
Wenzong Zhao
09/17/2012
Barnes and Nobles Thursday 7-9pm
Oce Hours: Monday 2-3pm and by Appointment
Lecture 4
1. Transport Problem
2. City Planning
3. Bridge Problem
4. etc.
Question 1: Are roads
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyoun
Wenzong Zhao
09/20/2012
Major Change: grader now, start collecting homework
(soon, not yet decided, no more quizzes, hw instead of quizzes)
(No class next week, instead, 2 lectures posted online)
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyan
11/05/2012
Midterm #2 will be Thursday, November 15, will cover everything since Midterm #1 up to November 12
Tournaments
Round Robin: All teams play one another.
Modelled as graph: Vertices are t
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyan
10/25/2012
Note : Part of todays lecture is not covered in the book.
Will not be at Barnes and Noble tonight
We know that (G) (G).
Question : Can (G) = (G)?
Theorem : If G is a connected graph suc
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyan
10/22/2012
Midterm Exam I returned: out of: 95, average: 63
Connectivity and edge-connectivity
Example A:
Observation :
a) If we cut any edge in a tree, then the tree becomes disconnected.
b) a) i
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyan
10/18/2012
Not at Barnes & Noble tonight
Tomorrow: 1:30 Q&A Session in ARC 206 (similar to oce hours)
Lecture 10: Spanning Trees (again)
Example :
Denition : Given a connected graph G, T is a span
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyoun
10/11/2012
Comment: 7-9pm in Barnes and Noble tonight
Reminder: Review Session 1:30pm, ARC 206, no review material prepared, so come with questions
Exam will cover up to this lecture (mostly on H
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyoun
10/08/2012
Lecture 8: Trees
Recall:
Theorem : An edge e is a bridge if and only if e is not on any cycle.
Example :
Denition : A tree is a graph with no cycles.
Propostition: Every edge e of a tr
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyoun
10/04/2012
Review Class is the following Friday, 10/12/2012,
it will be a review session for the Midterm on Monday, 10/15/2012
TIME: 01:30 P 03:00 ANTICIPATED ATTENDANCE:
CAMPUS: BUSCH
EVENT TYPE
Notes for 640-428 Graph Theory
Instructor: Grigor Sargsyoun
10/01/2012
Makeup classes: 1:30 to 2:50, next two Fridays, 10/05, 10/12
Midterm Exam: Thursday, 10/11
Mostly based on HW (1 or 2 questions that are more tricky)
1 problem stating the dentions
Lec