On the Complexity of Finding a Minimum Cycle Cover of a Graph

We prove that the problem of finding a cycle cover of smallest total length is NP-hard. This confirms a conjecture of Itai, Lipton, Papadimitriou, and Rodeh from 1981.

[1]  Cheng Zhao.  Smallest (1, 2)-eulerian weight and shortest cycle covering , 1994, J. Graph Theory.

[2]  Genghua Fan.  Covering Graphs by Cycles , 1992, SIAM J. Discret. Math..

[3]  J. A. Bondy,et al.  Small Cycle Double Covers of Graphs , 1990 .

[4]  Richard J. Lipton,et al.  Covering Graphs by Simple Circuits , 1981, SIAM J. Comput..

[5]  Ian Holyer,et al.  The NP-Completeness of Edge-Coloring , 1981, SIAM J. Comput..