Graphs, colourings and the four-colour theorem
Oxford
University Press
(2002). £19.50 paperback (ISBN 0198510624) or £45.00 hardback
(ISBN 0198510616).
Corrections
The following errors and misprints have already been found. If you have
found any others, please email me: R.A.Wilson [ at qmul.ac.uk]
- p. 29: in line 1, 'negative' should read 'non-positive', and in Lemma
3.17 and Proposition 3.18 the summation should start with i=0.
- p. 38: the proof of Theorem 4.11 is incomplete, as it does not deal
with the case when the collapsing produces a multigraph which is not a graph.
- p. 57: in Exercise 5.10, Delta = Delta(G).
- p. 61: the proof of Corollary 6.2 is inaccurate, as the case p-q+r=1
may also occur. It is better to continue adding edges until the faces are
2-cells, when p-q+r=0.
- p. 120: the Kempe-chain arguments in the proof of Theorem 10.9 are
wrong. In case 4, either there is a blue-green chain from v2 to
v7, in which case we can change v1 to yellow; or there
is a blue-green chain from v5 to v7, in which case
we can change v6 to yellow; or there is neither, in which case
we can change v7 to green. In all three cases, we can now complete
the colouring. Similarly, in case 5, either there is a blue-yellow chain
from v2 to v5, in which case we can change v3
to red and v4 to green; or there is a blue-yellow chain from v
5 to v7, in which case we can change v6 to red,
and we are back in case 3; or there is neither, in which case we can change
v5 to yellow. In all cases, we can now complete the colouring.
A (possibly less up to date) version of this list is also available as a
LaTeX
file, a dvi
file, and a postscript
file.
My thanks to Marijke van Gans and Peter Kratz for notifying me of errors.
Created with Netscape Communicator 4.05 on 27th February
2003.
Last updated 11th October 2004.