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arXiv · 1911.12179

Extended Formulations for Stable Set Polytopes of Graphs Without Two Disjoint Odd Cycles

Michele Conforti·Samuel Fiorini·Tony Huynh·Stefan Weltge
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Abstract

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 $G$.

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Michele Conforti, Samuel Fiorini, Tony Huynh, Stefan Weltge. 2019-11-27. Extended Formulations for Stable Set Polytopes of Graphs Without Two Disjoint Odd Cycles. https://doi.org/10.1007/s10107-021-01635-0

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