Approximate min-max relations on plane graphs

Authors:
Jie Ma;Xingxing Yu;Wenan Zang
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, USA 30332;School of Mathematics, Georgia Institute of Technology, Atlanta, USA 30332;Department of Mathematics, The University of Hong Kong, Hong Kong, China
Venue:
Journal of Combinatorial Optimization
Year:
2013

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Abstract

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