Approximation Algorithms and Hardness Results for Cycle Packing Problems Michael Krivelevich Tel Aviv University and Zeev Nutov Open University of Israel and Mohammad R. Salavatipour University of Alberta and Jacques Verstraete University of Waterloo and Raphael Yuster University of Haifa A preliminary version of this paper appeared as two separate papers, titled: “Approximation Algorithms for Cycle Packing Problems” in Proceedings of the 16th Annual ACM-SIAM Sympo- sium on Discrete Algorithms, Vancouver, Canada, 2005, and “Disjoint Cycles: Integrality Gap, Hardness, and Approximation” in Proceedings of 11th Conference on Integer Programming and Combinatorial Optimization, Berlin, Germany, 2005. Authors’ addresses: Michael Krivelevich, Department of Mathematics, Tel Aviv University, Tel Aviv, Israel. E-mail: krivelev@post.tau.ac.il. Research supported in part by USA-Israel BSF Grant 2002-133, and by grant 64/01 from the Israel Science Foundation. Zeev Nutov, Department of Computer Science, The Open University of Israel, Tel Aviv, Israel. E-mail: nutov@openu.ac.il. Mohammad R. Salavatipour, Department of Computing Science, University of Alberta, Edmon- ton, AB T6G2E8, Canada. E-mail: mreza@cs.ualberta.ca. Supported by NSERC and a faculty startup grant from University of Alberta. Jacques Verstraete, Department of Combinatorics and Optimization, University of Waterloo, Wa- terloo, ON N2L3G1, Canada. E-mail: jverstra@math.uwaterloo.ca. Supported by NSERC Dis- covery Grant 298149. Raphael Yuster, Department of Mathematics, University of Haifa, Haifa 31905, Israel. E-mail: raphy@research.haifa.ac.il. Permission to make digital/hard copy of all or part of this material without fee for personal or classroom use provided that the copies are not made or distributed for profit or commercial advantage, the ACM copyright/server notice, the title of the publication, and its date appear, and notice is given that copying is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior specific permission and/or a fee. c  20YY ACM 0000-0000/20YY/0000-0001 $5.00 ACM Journal Name, Vol. V, No. N, Month 20YY, Pages 1–0??.