**Tuesday, March 1,** **11am**** ET** (4pm GMT, 5am Wed NZDT)

**Louis Esperet**, G-SCOP Laboratory (CNRS, Grenoble)

**Packing and covering balls in planar graphs**

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**Abstract:**

The set of all vertices at distance at most $r$ from a vertex $v$ in a graph $G$ is called an $r$-ball. We prove that the minimum number of vertices hitting all $r$-balls in a planar graph $G$ is at most a constant (independent of $r$) times the maximum number of vertex-disjoint $r$-balls in $G$. This was conjectured by Estellon, Chepoi and Vaxès in 2007. Our result holds more generally for any proper minor-closed class, and for systems of balls of arbitrary (and possibly distinct) radii.

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##### Joint work with N. Bousquet, W. Cames van Batenburg, G. Joret, W. Lochet, C. Muller, and F. Pirot.