LTCC Course: Graph Theory
General information about
the LTCC course on Graph Theory
This is a course intended for first year research students in Mathematics,
provided for the London Taught Course Centre (LTCC). See the LTCC website for full details of the
objectives and activities of the LTCC, and of other available courses.
See 
here for
general information about the course -- much of the
information in the handout is repeated below.
Teachers responsible:
Peter Allen
and Jozef
Skokan,
Department of Mathematics, LSE
Lectures:
30 September - 28 October 2013
in De
Morgan House, London.
General description
Objectives
Our aims in this course are twofold. First, to discuss some of the major
results of graph theory, and to provide an introduction to the language,
methods and terminology of the subject. Second, to emphasise various
approaches (algorithmic, probabilistic, etc) that have proved fruitful in
modern graph theory: these modes of thinking about the subject have also
proved successful in other areas of mathematics, and we hope that students
will find the techniques learnt in this course to be useful in other areas
of mathematics.
Reading material
Below is a collection of books, including some that can be accessed online.
Any one of these textbooks should give sufficient reading material. The
code before each book will be used in the table of contents below.
- B&M
- J.A. Bondy and U.S.R. Murty, Graph Theory. Springer (2008).
A thorough and well-written textbook covering most parts of modern graph
theory. In many institutes you will be able to read this book online. Just
go to www.springerlink.com/content/978-1-84628-970-5.
Long ago, Bondy and Murty wrote one of the classic textbooks on graph
theory: Graph Theory with Applications. North Holland (1976). This
book is out of print (and has been out of print for ages). But the full
text is available online for personal use. You can download it from here.
- Diestel
- Reinhard Diestel, Graph Theory (1st, 2nd, 3rd, or 4th edition).
Springer-Verlag (1997, 2000, 2005, 2010).
Although this book is still in print, the author has made sure that a
restricted version is available online as well. See diestel-graph-theory.com/. All
editions are suitable for this course. References in the notes will refer
to the 4th edition (which is the same as the one you can download most
parts of).
- Bollobas
- Bela Bollobas, Modern
Graph Theory, Springer-Verlag (1998).
This is another classic textbook aimed at students at this level, and is
suitable for the course.
Pre-requisites
Many people attending the course will have taken an introductory course in
graph theory or discrete mathematics before, and we propose to assume a
certain amount of basic knowledge.
Specifically, we expect students attending these lectures to be familiar
with the following notions:
graphs; trees; paths; cycles; vertex degree; connectedness; bipartite
graphs; complete graphs; subgraphs.
Those requiring a quick refresher are advised to look at the introductory
chapter of any of the books listed above, before the course starts.
Contents, notes, and answers to exercises
Below are notes for this course. Some of them are from last year, and will
be replaced in due course. It is likely that there will be some small
changes this year, including possibly some rearrangement of the topics.
Examination questions
2012
examination, with solutions.
And the 2013
exam, of course also with solutions.
Copyright © Jan van den Heuvel, Jozef Skokan & London School of Economics and
Political Science 2008 - 2013
Last modified: Oct 30 11:06:03 BST 2013