, Volume 26, Issue 1, pp 127-134,
Open Access This content is freely available online to anyone, anywhere at any time.

Approximate min-max relations on plane graphs

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.

X. Yu supported in part by the National Security Agency of the US.
W. Zang supported in part by the Research Grants Council of Hong Kong.