Extended formulations for stable set polytopes of graphs without two disjoint odd cycles

Let G be an n -node graph without two disjoint odd cycles. The algorithm of Artmann, Weismantel and Zenklusen (STOC’17) for bimodular integer programs can be used to find a maximum weight stable set in G in strongly polynomial time. Building on structural results characterizing sufficiently connecte...

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Bibliographic Details
Published in:Mathematical programming 2022-03, Vol.192 (1-2), p.547-566
Main Authors: Conforti, Michele, Fiorini, Samuel, Huynh, Tony, Weltge, Stefan
Format: Article
Language:English
Subjects:
Algorithms
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Full Length Paper
Graphs
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Polynomials
Polytopes
Theoretical
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Summary:Let G be an n -node graph without two disjoint odd cycles. The algorithm of Artmann, Weismantel and Zenklusen (STOC’17) for bimodular integer programs can be used to find a maximum weight stable set in G in strongly polynomial time. Building on structural results characterizing sufficiently connected graphs without two disjoint odd cycles, we construct a size- O ( n 2 ) extended formulation for the stable set polytope of G .
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-021-01635-0