Journal of Combinatorial Optimization

, Volume 26, Issue 1, pp 127-134

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Approximate min-max relations on plane graphs

  • Jie MaAffiliated withSchool of Mathematics, Georgia Institute of Technology
  • , Xingxing YuAffiliated withSchool of Mathematics, Georgia Institute of Technology
  • , Wenan ZangAffiliated withDepartment of Mathematics, The University of Hong Kong Email author 


Let G be a plane graph, let τ(G) (resp. τ′(G)) be the minimum number of vertices (resp. edges) that meet all cycles of G, and let ν(G) (resp. ν′(G)) be the maximum number of vertex-disjoint (resp. edge-disjoint) cycles in G. In this note we show that τ(G)≤3ν(G) and τ′(G)≤4ν′(G)−1; our proofs are constructive, which yield polynomial-time algorithms for finding corresponding objects with the desired properties.


Plane graph Feedback set Cycle Approximate min-max relation