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Approximate min-max relations on plane graphs

Author

Listed:
  • Jie Ma

    (Georgia Institute of Technology)

  • Xingxing Yu

    (Georgia Institute of Technology)

  • Wenan Zang

    (The University of Hong Kong)

Abstract

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.

Suggested Citation

  • Jie Ma & Xingxing Yu & Wenan Zang, 2013. "Approximate min-max relations on plane graphs," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 127-134, July.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-011-9440-0
    DOI: 10.1007/s10878-011-9440-0
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