Contemporary Combinatorics

This volume is a collection of survey papers in combinatorics that have grown out of lectures given in the workshop on Probabilistic Combinatorics at the Paul Erdös Summer Research Center in Mathematics in Budapest. The papers, reflecting the many facets of modern-day combinatorics, will be appreciated by specia- lists and general mathematicians alike: assuming relatively little background, each paper gives a quick introduction to an active area, enabling the reader to learn about the fundamental results and appreciate some of the latest developments. An important feature of the articles, very much in the spirit of Erdös, is the abundance of open problems.

1. N. Alon: Graph Powers.- 2. J. Beck: TIC-TAC-TOE.- 3. R. Arratia: On the Amount of Dependence in the Prime Factorization of a Uniform Random Integer.- 4. B. Bollobas/L. Pebody/D. Weinreich: A State Space Definition of the HOMFLY Invariant.- 5. G. Brightwell/P. Winkler: Random Colorings of a Cayley Tree.- 6. S. Janson: On Concentration of Probability.- 7. B. Bollobas/A.D. Scott: Better Bounds for Max Cut.- 8. D. Coppersmith/ G.B. Sorkin: On the Expected Incremental Cost of a Minimum Assignment.