Generating and Counting Hamilton Cycles in Random Regular Graphs

∗Department of Mathematics, Carnegie Mellon University. Supported in part by NSF grants CCR9024935 and CCR9225008. †Department of Computer Science, University of Edinburgh, The King’s Buildings, Edinburgh EH9 3JZ, Uunited Kingdom. Supported in part by grant GR/F 90363 of the UK Science and Engineering Research Council, and Esprit Working Group 7097 “RAND.” ‡Department of Mathematics, Carnegie Mellon University. Supported in part by NSF grant CCR9225008. §Department of Computer Science, University of Georgia, Athens GA30602 ¶Department of Mathematics, University of Melbourne, Parkville, VIC3052 An event En is said to occur whp (with high probability) if Pr(En) = 1 − o(1) as n −→∞.