On finding two-connected subgraphs in planar graphs

Authors:
J.Scott Provan
Affiliations:
Department of Operations Research, University of North Carolina, CB 3180, 210 Smith Building, Chapel Hill, NC 27599-3180 USA
Venue:
Operations Research Letters
Year:
1997

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Abstract

We consider a basic problem in the design of reliable networks, namely, that of finding a minimum-weight 2-connected subgraph spanning a given set K of vertices in a planar graph. We show a relationship between this problem and that of finding shortest trails and cycles enclosing K, and derive a polynomial-time algorithm in the case when the vertices of K all lie on the same face.