The Co-2-plex Polytope and Integral Systems

$k$-plexes are cohesive subgraphs which were introduced to relax the structure of cliques. A co-$k$-plex is the complement of a $k$-plex and is therefore similar to a stable set. This paper derives the co-2-plex analogue for certain properties of the stable set polytope. We also describe a class of 0-1 matrices $A$ for which the polytope $\{x\in\mathbf{R}^n_+\mid Ax\leq 2,$ $x\leq 1\}$ is integral.

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