*Erdös on Graphs*introduces some of the unsolved graph theory problems Paul Erdös helped to frame, with chapters on "Ramsey Theory", "Extremal Graph Theory", "Coloring, Packing, and Covering", "Random Graphs and Graph Enumeration", "Hypergraphs", and "Infinite Graphs".

In presenting these problems, Chung and Graham include exposition of the background needed to understand them, summarising earlier work by Erdös and others. Footnotes give references into the mathematical literature for those who want the full details. And some lighter reading is provided by a preface introducing Erdös and an afterword by Andrew Vázsonyi with twenty pages of "Erdös stories" (and a brief foray into projective geometry).

The mathematics is fairly dense, but the dependencies between results
are not deep and a superficial grasp of a section won't prevent further
reading. Graph theory also lends itself to relatively easy visualisation,
and the only essential background is a good grasp of combinatorics and
basic number theory and algebra. *Erdös on Graphs* should be within
the reach of talented undergraduates.

August 2007

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