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arXiv · 1211.0039

A Semidefinite Approach to the $K_i$ Cover Problem

João Gouveia·James Pfeiffer
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Abstract

We apply theta body relaxations to the $K_i$-cover problem and show polynomial time solvability for certain classes of graphs. In particular, we give an effective relaxation where all $K_i$-$p$-hole facets are valid, and study its relation to an open question of Conforti et al. For the triangle free problem, we show for $K_n$ that the theta body relaxations do not converge by $(n-2)/4$ steps; we also prove for all $G$ an integrality gap of 2 for the second theta body.

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João Gouveia, James Pfeiffer. 2014-02-01. A Semidefinite Approach to the $K_i$ Cover Problem. https://arxiv.org/abs/1211.0039

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