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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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What is the LP gap of vertex cover in planar graphs?

The vertex cover LP gap is $\frac32$ for planar graphs. The $\frac32$ follows by looking at an extreme point optimal LP solution with values in $\{0, \frac12, 1\}$. Let $V_{i}$ be the set of vertices …
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