Almosttwodecadeshavepassedsincetheappearanceofthosegrapht- ory texts
that still set the agenda for most introductory courses taught today.
The canon created by those books has helped to identify some
main?eldsofstudyandresearch, andwilldoubtlesscontinuetoin?uence the
development of the discipline for some time to come. Yet much has
happened in those 20 years, in graph theory no less thanelsewhere:
deepnewtheoremshavebeenfound, seeminglydisparate methods and results
have become interrelated, entire new branches have arisen. To name just
a few such developments, one may think of how the new notion of list
colouring has bridged the gulf between inva- ants such as average degree
and chromatic number, how probabilistic methods andtheregularity
lemmahave pervadedextremalgraphtheory and Ramsey theory, or how the
entirely new ?eld of graph minors and tree-decompositions has brought
standard methods of surface topology to bear on long-standing
algorithmic graph problems. Clearly, then, the time has come for a
reappraisal: what are, today, the essential areas, methods and results
that should form the centre of an introductory graph theory course
aiming to equip its audience for the most likely developments ahead? I
have tried in this book to o?er material for such a course. In view of
the increasing complexity and maturity of the subject, I have broken
with the tradition of attempting to cover both theory and app- cations:
this book o?ers an introduction to the theory of graphs as part of
(pure) mathematics; it contains neither explicit algorithms nor 'real
world' applications.
