Combinatorics: Solutions, Additions, Corrections

This page relates to the book Combinatorics: Topics, Techniques, Algorithms by Peter J. Cameron, Cambridge University Press, 1994 (reprinted 1996). The ISBN is

0 521 45133 7 (hardback)
0 521 45761 0 (paperback).

Bibliographical details are given here.

You can

download solutions to the exercises,
read about further topics (this is in preparation),
find more problems and exercises, or
get a list of misprints.

Solutions to the exercises

The solutions are in PDF format: there is one file for each chapter. Only the first eleven chapters are available as yet (work in progress on the remainder), and detailed solutions to projects are not given.

Solutions to the remaining exercises are in preparation.

From the book

Here are LaTeX picture files for some of the diagrams in the book:

The 7-point STS (p. 108)
The Petersen graph (wih fivefold symmetry) (p. 183)
The Petersen graph (with threefold symmetry) (p. 243)
The Desargues configuration (p. 133)
The Pappus configuration (p. 133)

Further topics

This section will grow! I hope to outline such things as a proof of Dilworth's Theorem from Hall's (p. 196); Schnyder's Theorem, that a graph is planar if and only if its incidence poset has dimension at most 3 (p. 207); Wilf's inclusion-exclusion formula for the chromatic polynomial of a graph.

There are many interesting links between several of the topics mentioned in the book: graph colourings (p. 294), trees and forests (p. 162), matroids (p. 203), finite geometries (chapter 9), and codes (chapter 17, especially Section 17.7). Here is a short article describing some of these links, in PDF format.

Here are some curiosities about Fibonacci numbers, which are not as well known as they deserve to be, based on a conversation with John Conway. You can also learn more about Fibonacci numbers and related things at the Fibonacci pages at the University of Surrey.

Here is a proof of the Erdös-Ko-Rado theorem.

Problems

A collection of exercises is in preparation.

I have an idiosyncratic collection of research problems, with comments on the current state of knowledge, in my problem list. See especially problems 6, 12 and 18 in this list.

Further references

An update of the list of references:

L. W. Beineke and R. J. Wilson (editors), Graph Connections: Relations between graph theory and other parts of mathematics, Oxford University Press, 1997.
R. L. Graham and J. Nesetril (editors), The Mathematics of Paul Erdös, (2 volumes), Springer, Berlin, 1997.
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press, 1998.

Check the file containing further quotations related to combinatorics.