Optimization Letters

, Volume 13, Issue 2, pp 445–448 | Cite as

On approximating maximum covering cycles in undirected graphs

  • Dirk BriskornEmail author
Short Communication


We consider the problem to find a cycle in an undirected graph such that a maximum number of nodes is in the cycle or adjacent to a node in the cycle. The problem is known to be NP-hard and we strengthen this result by showing that there is no constant factor approximation algorithm unless \(P=NP\).


Undirected graphs Maximum covering cycle Approximation 


  1. 1.
    Álvarez-Miranda, E., Sinnl, M.: A branch-and-cut algorithm for the maximum covering cycle problem. Ann. Oper. Res.
  2. 2.
    Grosso, A., Salassa, F., Vancroonenburg, W.: Searching for a cycle with maximum coverage in undirected graphs. Optim. Lett. 10, 1493–1504 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Karger, D., Motwani, R., Ramkumar, G.D.S.: On approximating the longest path in a graph. Algorithmica 18, 82–98 (1997)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lehrstuhl für BWL, insbesondere Produktion und LogistikBergische Universität WuppertalWuppertalGermany

Personalised recommendations