On the feedback vertex set polytope of a series–parallel graph

Samuel Fiorini,Odile Marcotte

doi:10.1016/j.disopt.2009.01.004

On the feedback vertex set polytope of a series–parallel graph

Samuel Fiorini, Odile Marcotte

Open Access

https://doi.org/10.1016/j.disopt.2009.01.004

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Journal: Discrete Optimization	Publication Date: Feb 28, 2009
License type: elsevier-specific: oa user license

Affiliation: Université Libre de Bruxelles, HEC Montréal, Université du Québec à Montréal, Group for Research in Decision Analysis

#Minimum Weight Feedback Vertex Set #Series Parallel Graph + Show 8 more

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Abstract

The minimum weight feedback vertex set problem (FVS) on series–parallel graphs can be solved in O ( n ) time by dynamic programming. This solution, however, does not provide a “nice” certificate of optimality. We prove a min–max relation for FVS on series–parallel graphs with no induced subdivision of K 2 , 3 (a class of graphs containing the outerplanar graphs), thereby establishing the existence of nice certificates for these graphs. Our proof relies on the description of a complete set of inequalities defining the feedback vertex set polytope of a series–parallel graph with no induced subdivision of K 2 , 3 . We also prove that many of the inequalities described are facets of this polytope.

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